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

Author： Neretin Yu.  

Publisher： Springer Publishing Company

ISSN： 0016-2663

Source： Functional Analysis and Its Applications, Vol.39, Iss.2, 2005-04, pp. : 106-119

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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 2. 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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