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  • 1. Deift, Percy
    et al.
    Östensson, Jörgen
    A Riemann-Hilbert approach to some theorems on Toeplitz operators and orthogonal polynomials2006Inngår i: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 139, s. 144-171Artikkel i tidsskrift (Fagfellevurdert)
  • 2. Foerster, Clemens
    et al.
    Östensson, Jörgen
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Lieb-Thirring inequalities for higher order differential operators2008Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 281, nr 2, s. 199-213Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order gamma >= 3/4 for a fourth order operator in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of such operators, in dimensions greater than one. For the critical case gamma=1-1/(2l) in dimension d=1 with l >= 2 we prove the inequality L-l,r,d(o) < L-l,L-r,L-d, which holds in contrast to current conjectures.

  • 3. Hoppe, Jens
    et al.
    Laptev, Ari
    Östensson, Jörgen
    Solitons and the Removal of Eigenvalues for Fourth Order Differential Operators2006Inngår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247Artikkel i tidsskrift (Fagfellevurdert)
  • 4. Its, A. R.
    et al.
    Kuijlaars, A. B. J.
    Östensson, Jörgen
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Asymptotics for a special solution of the thirty fourth Painleve equation2009Inngår i: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 22, nr 7, s. 1523-1558Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In a previous paper we studied the double scaling limit of unitary random matrix ensembles of the form Z(n,N)(-1) vertical bar det M vertical bar(2 alpha)e(-NTrV(M)) dM with alpha > -1/2. The factor vertical bar det M vertical bar(2 alpha) induces critical eigenvalue behaviour near the origin. Under the assumption that the limiting mean eigenvalue density associated with V is regular, and that the origin is a right endpoint of its support, we computed the limiting eigenvalue correlation kernel in the double scaling limit as n, N -> infinity such that n(2/3)(n/N - 1) = O(1) by using the Deift-Zhou steepest descent method for the Riemann-Hilbert problem for polynomials on the line orthogonal with respect to the weight vertical bar x vertical bar(2 alpha)e(-NV(x)). Our main attention was on the construction of a local parametrix near the origin by means of the psi-functions associated with a distinguished solution u(alpha) of the Painleve XXXIV equation. This solution is related to a particular solution of the Painleve II equation, which, however, is different from the usual Hastings-McLeod solution. In this paper we compute the asymptotic behaviour of u(alpha)(s) as s -> +/-infinity. We conjecture that this asymptotics characterizes u(alpha) and we present supporting arguments based on the asymptotic analysis of a one-parameter family of solutions of the Painleve XXXIV equation which includes u(alpha). We identify this family as the family of tronquee solutions of the thirty fourth Painleve equation.

  • 5. Its, Alexander R.
    et al.
    Kuijlaars, Arno B. J.
    Östensson, Jörgen
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Critical Edge Behavior in Unitary Random Matrix Ensembles and the Thirty-Fourth Painleve Transcendent2008Inngår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, s. rnn017-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We describe a new universality class for unitary invariant random matrix ensembles. It arises in the double scaling limit of ensembles Z(n,N)(-1)vertical bar det M vertical bar (2 alpha)e(-NTrV(M)) dM, with alpha > -1/2, defined on n x n Hermitian matrices M. Assuming that the limiting mean eigenvalue density is regular and that the origin is a right endpoint of its support, we compute the limiting eigenvalue correlation kernel in the double scaling limit as n, N -> infinity such that n(2/3)(n/N-1) = O(1). We use the Deift-Zhou steepest descent method for the Riemann-Hilbert problem for polynomials orthogonal with respect to the weight vertical bar x vertical bar(2 alpha)e(-NV(x)). Our main attention is on the construction of a local parametrix near the origin by means of the psi-functions associated with a distinguished solution of the Painleve XXXIV equation.

  • 6. Laptev, Ari
    et al.
    Shterenberg, Roman
    Sukhanov, Vladimir
    Östensson, Jörgen
    Reflectionless potentials for an ordinary differential operator of order four2006Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 22, s. 135-153Artikkel i tidsskrift (Fagfellevurdert)
  • 7.
    Östensson, Jörgen
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Yafaev, Dimitri
    A trace formula for differential operators of arbitrary order2012Inngår i: Operator Theory: Advances and Applications, ISSN 1004-4469, E-ISSN 2334-2536, Vol. 218, s. 541-570Artikkel i tidsskrift (Fagfellevurdert)
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