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Some Continuous Analogs of the Expansion in Jacobi Polynomials and Vector-Valued Orthogonal Bases

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Abstract

We obtain the spectral decomposition of the hypergeometric differential operator on the contour Re z = 1/2. (The multiplicity of the spectrum of this operator is 2.) As a result, we obtain a new integral transform different from the Jacobi (or Olevskii) transform. We also construct an 3 F 2-orthogonal basis in a space of functions ranging in ℂ2. The basis lies in the analytic continuation of continuous dual Hahn polynomials with respect to the index n of a polynomial.

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Authors and Affiliations

  1. Math. Physics group, Institute of Theoretical and Experimental Physics, University of Vienna, Vienna

    Yu. A. Neretin

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 31–46, 2005

Original Russian Text Copyright © by Yu. A. Neretin

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Neretin, Y.A. Some Continuous Analogs of the Expansion in Jacobi Polynomials and Vector-Valued Orthogonal Bases. Funct Anal Its Appl 39, 106–119 (2005). https://doi.org/10.1007/s10688-005-0023-7

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  • DOI: https://doi.org/10.1007/s10688-005-0023-7

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