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

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 ₃F₂-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.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 31–46, 2005Original Russian Text Copyright © by Yu. A. Neretin