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Zbl 0777.44003
Duran, Antonio J.
Functions with given moments and weight functions for orthogonal polynomials. (English)
[J] Rocky Mt. J. Math. 23, No.1, 87-104 (1993). ISSN 0035-7596

The author gives a constructive technique to find smooth functions with given moments. Earlier in the well-known moment problem it was guaranteed that for every sequence of complex numbers there is a function of bounded variation with the given moments in these numbers.\par The author shows how these weight functions are found. He uses the technique of Fourier and Hankel transform in Schwartz spaces to establish the respective functions with the given moments. Namely, he finds the functions for the classical orthogonal polynomials: the Bessel polynomials, the Hermite polynomials, the Laguerre and generalized Laguerre polynomials, and the Jacobi polynomials.
[S.B.Yakubovich (Minsk)]

MSC 2000:: *44A60 Moment problems
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: Fourier transform; moments; Hankel transform; Schwartz spaces; orthogonal polynomials; Bessel polynomials; Hermite polynomials; Laguerre polynomials; Jacobi polynomials

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