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Analysis of a class of probability preserving measure algebras on compact intervals

Authors: William C. Connett and Alan L. Schwartz
Journal: Trans. Amer. Math. Soc. 320 (1990), 371-393
MSC: Primary 43A10; Secondary 34B25, 42C05
MathSciNet review: 961620
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Abstract: The measure algebras of the title are those which are also hypergroups with some regularity conditions. Examples include the convolutions associated with Jacobi polynomial series and Fourier Bessel series. It is shown here that there is a one-to-one correspondence between these hypergroups and a class of Sturm-Liouville problems which have the characters of the hypergroup as eigenfunctions. The interplay between these two characterizations allows a detailed analysis which includes a Hilb-type formula for the characters and asymptotic estimates for the Plancherel measure and the eigenvalues of the associated Sturm-Liouville problem.

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Keywords: Measure algebra, hypergroup, Sturm-Liouville problems
Article copyright: © Copyright 1990 American Mathematical Society

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