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Die Polynomlösungen spezieller partieller Differentialgleichungen

On polynomial solutions of certain partial differential equations

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Abstract

One of the main problems in the theory of orthogonal polynomials in several variables is the determination of partial differential equations which have the given polynomials as their solutions. In this note, we consider partial differential equations which are two-dimensional generalizations of the classical differential equation for the Chebyshev polynomials in one variable and we will give conditions for its polynomial solutions. In addition, we will be able to determine all polynomials of a given class which are solutions of the partial differential equation under consideration. In the last section, we establish a connection between the different polynomial solutions.

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Authors and Affiliations

  1. Institut für Algebra und Mathematische Strukturtheorie, Technische Universität Wien, Argentinierstraße 8, A-1040, Wien, Österreich

    H. K. Kaiser &  R. Lidl

Authors
  1. H. K. Kaiser
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  2. R. Lidl
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Kaiser, H.K., Lidl, R. Die Polynomlösungen spezieller partieller Differentialgleichungen. Monatshefte für Mathematik 81, 109–117 (1976). https://doi.org/10.1007/BF01301235

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  • DOI: https://doi.org/10.1007/BF01301235

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