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  • 1.
    Castro, Alejandro J.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Nazarbayev Univ, Dept Math, Astana 010000, Kazakhstan..
    Rodriguez-Lopez, Salvador
    Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden..
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    L2-solvability of the Dirichlet, Neumann and regularity problems for parabolic equations with time-independent Hölder-continuous coefficients2018In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 370, no 1, p. 265-319Article in journal (Refereed)
    Abstract [en]

    We establish the L-2-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with timeindependent Holder-continuous diffusion coefficients on bounded Lipschitz domains in R-n. This is achieved through the demonstration of invertibility of the relevant layer potentials, which is in turn based on Fredholm theory and a systematic transference scheme which yields suitable parabolic Rellich-type estimates.

  • 2.
    Castro, Alejandro, J.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Rodríguez-López, Salvador
    Staubach, Wolfgang
    L2 Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with time-independent Hölder-continuous coefficientsIn: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850Article in journal (Refereed)
    Abstract [en]

    We establish the $L^2$-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with time-independent H\"older-continuous diffusion coefficients, on bounded Lipschitz domains in $\mathbb{R}^n$. This is achieved through the demonstration of invertibility of the relevant layer-potentials which is in turn based on Fredholm theory and a systematic transference scheme which yields suitable parabolic Rellich-type estimates.

  • 3. Colliander, James
    et al.
    Staubach, Wolfgang
    Refinement of the Strichartz estimates and the L^2 mass concentration for 1-d quintic nonlinear Schrödinger equation2004Other (Other academic)
  • 4. Costin, Ovidiu
    et al.
    Schlag, Wilhelm
    Staubach, Wolfgang
    Tanveer, Saleh
    Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials2008In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 255, no 9, p. 2321-2362Article in journal (Refereed)
  • 5. Dong, Hongjie
    et al.
    Staubach, Wolfgang
    Unique continuation for the Schrödinger equation with gradient vector potentials2007In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 135, no 7, p. 2141-2149Article in journal (Refereed)
  • 6. Dos Santos Ferreira, David
    et al.
    Staubach, Wolfgang
    Global and local regularity of Fourier integral operators on weighted and unweighted spaces2014In: Memoirs of the American Mathematical Society, ISSN 0065-9266, E-ISSN 1947-6221, Vol. 229, no 1074Article in journal (Refereed)
  • 7. Greiner, Peter
    et al.
    Staubach, Wolfgang
    Wang, Wei
    A relative index on the space of 3-dimensional embeddable CR-structures of finite type2005In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 278, no 4, p. 379-400Article in journal (Refereed)
  • 8. Kenig, Carlos E.
    et al.
    Staubach, Wolfgang
    Ψ-pseudodifferential operators and estimates for maximal oscillatory integrals2007In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 183, no 3, p. 249-258Article in journal (Refereed)
  • 9. Michalowski, Nicholas
    et al.
    Rule, David J.
    Staubach, Wolfgang
    Weighted $L^p$ boundedness of pseudodifferential operators and applications2012In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 55, no 3, p. 555-570Article in journal (Refereed)
  • 10. Michalowski, Nicholas
    et al.
    Rule, David J.
    Staubach, Wolfgang
    Weighted norm inequalities for pseudo-pseudodifferential operators defined by amplitudes2010In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 258, no 12, p. 4183-4209Article in journal (Refereed)
  • 11. Michalowski, Nicholas
    et al.
    Rule, David
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Multilinear pseudo differential operators beyond Calderon-Zygmund theory2014In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 414, no 1, p. 149-165Article in journal (Refereed)
    Abstract [en]

    We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in Lebesgue spaces. These results generalise earlier work of the present authors concerning linear pseudo-pseudodifferential operators. Secondly, we investigate the boundedness of bilinear pseudodifferential operators with symbols in the Hormander S-p,delta(m) classes. These results are new in the case p < 1, that is, outwith the scope of multilinear Calderon-Zygmund theory. (C) 2014 Elsevier Inc. All rights reserved.

  • 12. Radnell, David
    et al.
    Schippers, Eric
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    A Hilbert manifold structure on the Weil-Petersson class Teichmuller space of bordered Riemann surfaces2015In: Communications in Contemporary Mathematics, ISSN 0219-1997, Vol. 17, no 4, article id 1550016Article in journal (Refereed)
    Abstract [en]

    We consider bordered Riemann surfaces which are biholomorphic to compact Riemann surfaces of genus g with n regions biholomorphic to the disk removed. We define a refined Teichmuller space of such Riemann surfaces (which we refer to as the WP-class Teichmuller space) and demonstrate that in the case that 2g + 2 - n > 0, this refined Teichmuller space is a Hilbert manifold. The inclusion map from the refined Teichm " uller space into the usual Teichm " uller space (which is a Banach manifold) is holomorphic. We also show that the rigged moduli space of Riemann surfaces with non-overlapping holomorphic maps, appearing in conformal field theory, is a complex Hilbert manifold. This result requires an analytic reformulation of the moduli space, by enlarging the set of non-overlapping mappings to a class of maps intermediate between analytically extendible maps and quasiconformally extendible maps. Finally, we show that the rigged moduli space is the quotient of the refined Teichmuller space by a properly discontinuous group of biholomorphisms.

  • 13. Radnell, David
    et al.
    Schippers, Eric
    Staubach, Wolfgang
    A Hilbert manifold structure on the Weil-Petersson class Teichmüller space of  bordered Riemann surfaces2015In: Communications in Contemporary Mathematics, ISSN 0219-1997Article in journal (Refereed)
    Abstract [en]

    We consider bordered Riemann surfaces which are biholomorphic to compact Riemann surfaces of genus g with n regions biholomorphic to the disk removed. We define a refined Teichmüller space of such Riemann surfaces (which we refer to as the WP-class Teichmüller space) and demonstrate that in the case that 2g + 2 − n > 0, this refined Teichmüller space is a Hilbert manifold. The inclusion map from the refined Teichmüllerspace into the usual Teichmüller space (which is a Banach manifold) is holomorphic. We also show that the rigged moduli space of Riemann surfaces with non-overlappingholomorphic maps, appearing in conformal field theory, is a complex Hilbert manifold. This result requires an analytic reformulation of the moduli space, by enlarging the set of non-overlapping mappings to a class of maps intermediate between analytically extendible mapsand quasiconformally extendible maps. Finally we show that the rigged moduli space is thequotient of the refined Teichmüller space by a properly discontinuous group of biholomorphisms.

  • 14.
    Radnell, David
    et al.
    Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
    Schippers, Eric
    Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Convergence of the Weil-Petersson metric on the Teichmüller space of bordered Riemann surfaces2017In: Communications in Contemporary Mathematics, ISSN 0219-1997, Vol. 19, no 1, article id 1650025Article in journal (Refereed)
    Abstract [en]

    Consider a Riemann surface of genus g bordered by n curves homeomorphic to the unit circle, and assume that 2g−2+n > 0. For such bordered Riemann surfaces, the authors have previously defined a Teichmüller space which is a Hilbert manifold and which is holomorphically included in the standard Teichmüller space.We show that any tangent vector can be represented as the derivative of a holomor-phic curve whose representative Beltrami differentials are simultaneously in L2 and L ,and furthermore that the space of (−1,1) differentials in L2 ∩L decomposes as a directsum of infinitesimally trivial differentials and L2 harmonic (−1,1) differentials. Thus thetangent space of this Teichmüller space is given by L2 harmonic Beltrami differentials.We conclude that this Teichmüller space has a finite Weil-Petersson Hermitian metric.Finally, we show that the aforementioned Teichmüller space is locally modeled on a spaceof L2 harmonic Beltrami differentials.

  • 15.
    Radnell, David
    et al.
    Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
    Schippers, Eric
    Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Dirichlet's problem and Sokhotski-Plemelj's jump formula on Weil-Petersson-Class quasidisks2016In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 41, no 1, p. 119-127Article in journal (Refereed)
    Abstract [en]

    We show the solvability of the Dirichlet problem on Weil–Petersson class quasidisks and establish a Sokhotski–Plemelj jump formula for Weil–Petersson class quasicircles. Furthermore we show that the resulting Cauchy projections are bounded. In both cases the boundary data belongs to a certain conformally invariant Besov space. Moreover we show that the WP-class quasicircles are chord-arc curves.

  • 16. Radnell, David
    et al.
    Schippers, Eric
    Staubach, Wolfgang
    Model of the Teichmüller space of genus zero by period mapsManuscript (preprint) (Other academic)
    Abstract [en]

    We define a generalized Grunsky operator corresponding to $n$ non-overlapping quasiconformally extendible conformal maps of the disk into the sphere. We show that the Grunsky operator elegantly characterizes the Dirichlet space of the sphere minus $n$ quasicircles. Furthermore, we define a map from the Teichmüller space of the sphere minus $n$ simply connected regions into the direct product of the Teichmüller space of the sphere minus $n$ points with the unit ball in the Banach space of linear maps between a direct sum of Dirichlet spaces of disks. We show that this map is holomorphic and show that it is injective up to a discrete action by a subgroup of the (quasiconformal) Teichmüller modular group. This extends the classical period mapping of compact surfaces to surfaces of genus $0$ bordered by $n$ closed curves.

  • 17.
    Radnell, David
    et al.
    Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
    Schippers, Eric
    Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials2017In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 132, no 1, p. 229-245Article in journal (Refereed)
    Abstract [en]

    Let Σ be a Riemann surface of genus g bordered by n curves homeomorphic to the circle S1 . Consider quasiconformal maps f : Σ → Σ1 such that the restriction to each boundary curve is a Weil-Petersson class quasisymmetry. We show that any such f is homotopic to a quasiconformal map whose Beltrami differential is L2 with respect to the hyperbolic metric on Σ. The homotopy H(t,·) : Σ → Σ1 is independent of t on the boundary curves; that is H(t,p) = f(p) for all p ∈ ∂Σ.

  • 18. Radnell, David
    et al.
    Schippers, Eric
    Staubach, Wolfgang
    Quasiconformal Teichmüller theory as an analytical foundation for two dimensional conformal field theoryIn: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627Article in journal (Refereed)
    Abstract [en]

    The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and the sewing operation. We survey the recent and careful study of these objects, which has led to significant connections with quasiconformal Teichmüller theory and geometric function theory. In particular we propose that the natural analytic setting for conformal field theory is the moduli space of Riemann surfaces with so-called Weil-Petersson class parametrizations. A collection of rigorous analytic results is advanced here as evidence. This class of parametrizations has the required regularity for CFT on one hand, and on the other hand are natural and of interest in their own right in geometric function theory.

  • 19.
    Radnell, David
    et al.
    Aalto Univ, Dept Math & Syst Anal, Aalto, Finland.
    Schippers, Eric
    Univ Manitoba, Dept Math, Winnipeg, Canada.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Quasiconformal Teichmüller theory as an analytical foundation for two-dimensional conformal field theor2017In: Lie Algebras, Vertex Operator Algebras, And Related Topics / [ed] Barron, Katrina; Jurisich, Elizabeth; Milas, Antun & Misra, Kailash, American Mathematical Society (AMS), 2017, p. 205-238Conference paper (Refereed)
    Abstract [en]

    The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and the sewing operation. We survey the recent and careful study of these objects, which has led to significant connections with quasiconformal Teichmuller theory and geometric function theory. In particular we propose that the natural analytic setting for conformal field theory is the moduli space of Riemann surfaces with so-called WeilPetersson class parametrizations. A collection of rigorous analytic results is advanced here as evidence. This class of parametrizations has the required regularity for CFT on one hand, and on the other hand are natural and of interest in their own right in geometric function theory.

  • 20.
    Radnell, David
    et al.
    Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland..
    Schippers, Eric
    Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada..
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Weil-Petersson class non-overlapping mappings into a Riemann surface2016In: Communications in Contemporary Mathematics, ISSN 0219-1997, Vol. 18, no 4, article id 1550060Article in journal (Refereed)
    Abstract [en]

    For a compact Riemann surface of genus g with n punctures, consider the class of n-tuples of conformal mappings (phi(1),..., phi(n)) of the unit disk each taking 0 to a puncture. Assume further that (1) these maps are quasiconformally extendible to C, (2) the pre-Schwarzian of each phi(i) is in the Bergman space, and (3) the images of the closures of the disk do not intersect. We show that the class of such non-overlapping mappings is a complex Hilbert manifold.

  • 21.
    Rodriguez-Lopez, Salvador
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Rule, David
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    A Seeger-Sogge-Stein theorem for bilinear Fourier integral operators2014In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 264, p. 1-54Article in journal (Refereed)
    Abstract [en]

    We establish the regularity of bilinear Fourier integral operators with bilinear amplitudes in S-1,0(m) (n, 2) and non-degenerate phase functions, from L-P x L-q -> L-r under the assumptions that m <= -(n - 1)(vertical bar 1/p - 1/2 vertical bar + vertical bar 1/q - 1/2 vertical bar) and 1/p + 1/q = 1/r. This is a bilinear version of the classical theorem of Seeger-Sogge-Stein concerning the L-P boundedness of linear Fourier integral operators. Moreover, our result goes beyond the aforementioned theorem in that it also includes the case of quasi-Banach target spaces.

  • 22.
    Rodriguez-Lopez, Salvador
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Rule, David
    Linköping University.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    On The Boundedness Of Certain Bilinear Oscillatory Integral Operators2015In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 367, no 10, p. 6971-6995Article in journal (Refereed)
    Abstract [en]

    We prove the global L2xL->L1boundedness of bilinear oscillatory integral operators with amplitudes satisfying a Hörmander type condition and phases satisfying appropriate growth as well as the strong non-degeneracy conditions. This is anextension of the corresponding result of R. Coifman and Y. Meyer for bilinear pseudo-dierential operators, to the case of oscillatory integral operators.

  • 23.
    Rodriguez-Lopez, Salvador
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Estimates for rough Fourier integral and pseudodifferential operators and applications to the boundedness of multilinear operators2013In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 264, no 10, p. 2356-2385Article in journal (Refereed)
    Abstract [en]

    We study the boundedness of rough Fourier integral and pseudodifferential operators, defined by general rough Hörmander class amplitudes, on Banach and quasi-Banach LpLp spaces. Thereafter we apply the aforementioned boundedness in order to improve on some of the existing boundedness results for Hörmander class bilinear pseudodifferential operators and certain classes of bilinear (as well as multilinear) Fourier integral operators. For these classes of amplitudes, the boundedness of the aforementioned Fourier integral operators turn out to be sharp. Furthermore we also obtain results for rough multilinear operators.

  • 24.
    Rodriguez-Lopez, Salvador
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Some endpoint estimates for bilinear paraproducts and applications2015In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 421, no 2, p. 1021-1041Article in journal (Refereed)
    Abstract [en]

    In this paper we establish the boundedness of bilinear paraproducts on local BMO spaces. As applications, we also investigate the boundedness of bilinear Fourier integral operators and bilinear Coifman-Meyer multipliers on these spaces and also obtain a certain end-point result concerning Kato Ponce type estimates.

  • 25. Schippers, Eric
    et al.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    A symplectic functional analytic proof of the conformal welding theorem2015In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 1, p. 265-278Article in journal (Refereed)
    Abstract [en]

    We give a new functional-analytic/symplectic geometric proof of the conformal welding theorem. This is accomplished by representing composition by a quasisymmetric map phi as an operator on a suitable Hilbert space and algebraically solving the conformal welding equation for the unknown maps f and g satisfying g o phi = f. The univalence and quasiconformal extendibility of f and g is demonstrated through the use of the Grunsky matrix.

  • 26. Schippers, Eric
    et al.
    Staubach, Wolfgang
    Comparison moduli spaces for Riemann surfaces2016In: New Trends and Open Problems in Complex Analysis and Dynamical SystemsArticle in journal (Other academic)
    Abstract [en]

    We define a kind of moduli space of nested surfaces and mappings, which we call a comparison moduli space. We review examples of such spaces in geometric function theory and modern Teichmüller theory, and illustrate how a wide range of phenomena in complex analysis are captured by this notion of moduli space. The paper includes a list of open problemss ranging from quite general theoretical questions to specific technical problems

  • 27.
    Schippers, Eric
    et al.
    Univ Manitoba, Dept Math, Canada..
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Harmonic reflection in quasicircles and well-posedness of a Riemann-Hilbert problem on quasidisks2017In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 448, no 2, p. 864-884Article in journal (Refereed)
    Abstract [en]

    A complex harmonic function of finite Dirichlet energy on a Jordan domain has boundary values in a certain conformally invariant sense, by a construction of H. Osborn. We call the set of such boundary values the Douglas-Osborn space. One may then attempt to solve the Dirichlet problem on the complement for these boundary values. This defines a reflection of harmonic functions. We show that quasicircles are precisely those Jordan curves for which this reflection is defined and bounded. We then use a limiting Cauchy integral along level curves of Green's function to show that the Plemelj-Sokhotski jump formula holds on quasicircles with boundary data in the Douglas-Osborn space. This enables us to prove the well-posedness of a Riemann-Hilbert problem with boundary data in the Douglas Osborn space on quasicircles.

  • 28.
    Schippers, Eric
    et al.
    Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Riemann boundary value problem on quasidisks, Faber isomorphism and Grunsky operator.2018In: Complex Analysis and Operator Theory, ISSN 1661-8254, E-ISSN 1661-8262, Vol. 12, no 2, p. 325-354Article in journal (Refereed)
    Abstract [en]

    Let Γ be a bounded Jordan curve with complementary components Ω ± . Weshow that the jump decomposition is an isomorphism if and only if Γ is a quasicircle. Wealso show that the Bergman space of L 2 harmonic one-forms on Ω + is isomorphic to thedirect sum of the holomorphic Bergman spaces on Ω + and Ω − if and only if Γ is a quasicircle.This allows us to derive various relations between a reflection of harmonic functions inquasicircles and the jump decomposition on the one hand, and the Grunsky operator, Faberseries and kernel functions of Schiffer on the other hand. It also leads to new interpretationsof the Grunsky and Schiffer operators. We show throughout that the most general settingfor these relations is quasidisks.

  • 29. Schippers, Eric
    et al.
    Staubach, Wolfgang
    Variation of Neumann and Green functions under homotopies of the boundary2009In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 173, p. 279-303Article in journal (Refereed)
  • 30.
    Schippers, Eric
    et al.
    Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada..
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Well-Posedness of a Rieman-Nhilbert Problem on d-Regular Quasidisks2017In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 42, no 1, p. 141-147Article in journal (Refereed)
    Abstract [en]

    We prove the well-posedness of a Riemann-Hilbert problem on d-regular quasidisks, with boundary data in a class of Besov spaces.

  • 31. Schippers, Eric
    et al.
    Staubach, Wolfgang
    Well-posedness of a Riemann-Hilbert problem on d-regular quasidisks2016In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383Article in journal (Refereed)
    Abstract [en]

    We prove the well-posedness of a Riemann-Hilbert problem on d-regular qua-sidisks, with boundary data in a class of Besov spaces.

  • 32. Schlag, Wilhelm
    et al.
    Soffer, Avy
    Staubach, Wolfgang
    Decay for the wave and Schrödinger evolutions on manifolds with conical ends. I2010In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 362, no 1, p. 19-52Article in journal (Refereed)
  • 33. Schlag, Wilhelm
    et al.
    Soffer, Avy
    Staubach, Wolfgang
    Decay for the wave and Schrödinger evolutions on manifolds with conical ends. II2010In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 362, no 1, p. 289-318Article in journal (Refereed)
  • 34. Staubach, Wolfgang
    Path integrals, microlocal analysis and the fundamental solution for Hörmander Laplacians2003Book (Other academic)
  • 35. Staubach, Wolfgang
    Pseudolocality and microlocality of general classes of pseudodifferential operators2001In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 223, p. 121-134Article in journal (Refereed)
  • 36. Staubach, Wolfgang
    Wiener path integrals and the fundamental solution for the Heisenberg Laplacian2003In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 91, p. 389-400Article in journal (Refereed)
1 - 36 of 36
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