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Kaijser, Sten
Publications (10 of 12) Show all publications
Kaijser, S. & Reinov, O. I. (2019). Some approximation properties and nuclear operators in spaces of analytical functions. ADVANCES IN OPERATOR THEORY, 4(1), 265-283
Open this publication in new window or tab >>Some approximation properties and nuclear operators in spaces of analytical functions
2019 (English)In: ADVANCES IN OPERATOR THEORY, ISSN 2538-225X, Vol. 4, no 1, p. 265-283Article in journal (Refereed) Published
Abstract [en]

We introduce and investigate a new notion of the approximation property AP([c]), where c = (c(n)) is an arbitrary positive real sequence, tending to infinity. Also, we study the corresponding notion of [c]-nuclear operators in Banach spaces. Some characterization of the AP([c]) in terms of tensor products, as well as sufficient conditions for a Banach space to have the AP([c]), are given. We give also sufficient conditions for a positive answer to the question: When it follows from the [c]-nuclearity of an adjoint operator the nuclearity of the operator itself. Obtained results are applied then to the study of properties of nuclear operators in some spaces of analytical functions. Many examples are given.

Place, publisher, year, edition, pages
TUSI MATHEMATICAL RESEARCH GROUP, 2019
Keywords
Nuclear operator, tensor product, approximation property, space of bounded analytical functions
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:uu:diva-367007 (URN)10.15352/aot.1805-1360 (DOI)000445969300013 ()
Available from: 2018-11-28 Created: 2018-11-28 Last updated: 2018-11-28Bibliographically approved
Musonda, J. & Kaijser, S. (2018). Three systems of orthogonal polynomials and L-2-boundedness of two associated operators. Journal of Mathematical Analysis and Applications, 459(1), 464-475
Open this publication in new window or tab >>Three systems of orthogonal polynomials and L-2-boundedness of two associated operators
2018 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 459, no 1, p. 464-475Article in journal (Refereed) Published
Abstract [en]

In this paper, we describe three systems of orthogonal polynomials belonging to the class of Meixner-Pollaczek polynomials, and establish some useful connections between them in terms of three basic operators that are related to them. Furthermore, we investigate boundedness properties of two other operators, both as convolution operators in the translation invariant case where we use Fourier transforms and for the weights related to the relevant orthogonal polynomials. We consider only the most important but also simplest case of L-2-spaces. However, in subsequent papers, we intend to extend the study to L-p-spaces (1 < p < infinity).

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018
Keywords
Orthonormal basis, Hilbert space, Convolution operator
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-338945 (URN)10.1016/j.jmaa.2017.10.040 (DOI)000418310900027 ()
Available from: 2018-01-18 Created: 2018-01-18 Last updated: 2018-01-18Bibliographically approved
Janson, S. & Kaijser, S. (2015). Higher moments of Banach space valued random variables. Memoirs of the American Mathematical Society, 238(1127), 1-110
Open this publication in new window or tab >>Higher moments of Banach space valued random variables
2015 (English)In: Memoirs of the American Mathematical Society, ISSN 0065-9266, E-ISSN 1947-6221, Vol. 238, no 1127, p. 1-110Article in journal (Refereed) Published
Abstract [en]

We define the k:th moment of a Banach space valued random variable as the expectation of its k: th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals. One of the problems studied is whether two random variables with the same injective moments (of a given order) necessarily have the same projective moments; this is of interest in applications. We show that this holds if the Banach space has the approximation property, but not in general. Several chapters are devoted to results in special Banach spaces, including Hilbert spaces, C(K) and D[0,1]. The latter space is non-separable, which complicates the arguments, and we prove various preliminary results on e.g. measurability in D[0,1] that we need. One of the main motivations of this paper is the application to Zolotarev metrics and their use in the contraction method. This is sketched in an appendix.

National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-287527 (URN)10.1090/memo/1127 (DOI)000372829500001 ()
Funder
Knut and Alice Wallenberg Foundation
Available from: 2016-04-25 Created: 2016-04-25 Last updated: 2017-11-30Bibliographically approved
Ekstig, K., Kaijser, S., Kiselman, C. O., Lindahl, L.-Å. & Vretblad, A. (2015). Sonja Lyttkens: Minnesord. Upsala Nya Tidning, 125(12), pp. B13-B13
Open this publication in new window or tab >>Sonja Lyttkens: Minnesord
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2015 (Swedish)In: Upsala Nya Tidning, Vol. 125, no 12, p. B13-B13Article in journal, News item (Other (popular science, discussion, etc.)) Published
Abstract [en]

Sonja Lyttkens was born in 1919 and died in 2014. She was the second woman to get a PhD in mathematics in Sweden, and the first to become a university lecturer.

National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-241692 (URN)
Available from: 2015-01-14 Created: 2015-01-15 Last updated: 2015-12-28Bibliographically approved
Bakan, A. & Kaijser, S. (2006). Hardy spaces for the strip.
Open this publication in new window or tab >>Hardy spaces for the strip
2006 (English)Report (Other (popular scientific, debate etc.))
Series
UUDM ; 2006:13
Identifiers
urn:nbn:se:uu:diva-23815 (URN)
Available from: 2007-02-01 Created: 2007-02-01
Kaijser, S., Nikolova, L. & Persson, L.-E. (2005). Hardy-type inequalities via convexity. MATHEMATICAL INEQUALITIES & APPLICATIONS, 8(3), 403-417
Open this publication in new window or tab >>Hardy-type inequalities via convexity
2005 (Swedish)In: MATHEMATICAL INEQUALITIES & APPLICATIONS, Vol. 8, no 3, p. 403-417Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-77574 (URN)
Available from: 2006-04-18 Created: 2006-04-18 Last updated: 2011-01-11
Persson, L.-E., Kaijser, S. & Nikolova, L. (2005). On Hardy-type inequalities via convexity. Math. Inequal. Appl (3), 403-417
Open this publication in new window or tab >>On Hardy-type inequalities via convexity
2005 (English)In: Math. Inequal. Appl, no 3, p. 403-417Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-77637 (URN)
Available from: 2006-04-18 Created: 2006-04-18 Last updated: 2011-01-11
Kaijser, S. (2004). Biography of Matts Essén.. Complex Var. Theory Appl. (49), 7-9
Open this publication in new window or tab >>Biography of Matts Essén.
2004 (English)In: Complex Var. Theory Appl., no 49, p. 7-9Article in journal (Other (popular scientific, debate etc.)) Published
Identifiers
urn:nbn:se:uu:diva-71119 (URN)
Available from: 2005-04-29 Created: 2005-04-29 Last updated: 2011-01-12
Blanco, A., Kaijser, S. & Ransford, T. J. (2004). Real interpolation of Banach algebras and factorization of weakly compact homomorphisms. Journal of functional analysis, 217(1), 126-141
Open this publication in new window or tab >>Real interpolation of Banach algebras and factorization of weakly compact homomorphisms
2004 (English)In: Journal of functional analysis, ISSN 1096-0783, Vol. 217, no 1, p. 126-141Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-71113 (URN)10.1016/j.jfa.2004.03.011 (DOI)
Available from: 2005-04-29 Created: 2005-04-29 Last updated: 2009-10-08Bibliographically approved
Kaijser, S., Persson, L.-E. & Öberg, A. (2002). On Carleman and Knopp's inequalities. Journal of Approximation Theory, 117(1), 140-151
Open this publication in new window or tab >>On Carleman and Knopp's inequalities
2002 (English)In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 117, no 1, p. 140-151Article in journal (Refereed) Published
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:uu:diva-44524 (URN)10.1006/jath.2002.3684 (DOI)
Available from: 2007-01-23 Created: 2007-01-23 Last updated: 2017-12-05Bibliographically approved
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