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Hermann Render

  1. Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas.

    Thu, 04/05/2012 - 15:01 — SomNambul
    Authors: Ognyan Kounchev, Hermann Render
    Subjects: Numerical Analysis
    Abstract

    The present paper has a twofold contribution: first, we introduce a new
    concept of Hardy spaces on a multidimensional complexified annular domain which
    is closely related to the annulus of the Klein-Dirac quadric important in
    Conformal Quantum Field Theory. Secondly, for functions in these Hardy spaces,
    we provide error estimate for the polyharmonic Gau\ss -Jacobi cubature
    formulas, which have been introduced in previous papers.

  2. Pad\'e approximation for a multivariate Markov transform.

    Wed, 12/07/2011 - 15:01 — SomNambul
    Authors: Ognyan Kounchev, Hermann Render
    Subjects: Numerical Analysis
    Abstract

    Methods of Pad\'e approximation are used to analyse a multivariate Markov
    transform which has been recently introduced by the authors, and which is
    generalizing the well-known in Spectral theory Stieltjes transform (Markov
    function) of one-dimensional measure. The first main result is a
    characterization of the rationality of the Markov transform via Hankel
    determinants. The second main result is a cubature formula for a special class
    of measures.

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