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Jacobi Polynomials and Related Hypergroup Structures

In: Probability Measures on Groups X

Author

Listed:
  • W. C. Connett

    (University of Missouri - St. Louis, Department of Mathematics and Computer Science)

  • C. Markett

    (Rheinisch-Westfälische Technische Hochschule Aachen, Lehrstuhl a für Mathematik)

  • A. L. Schwartz

    (University of Missouri - St. Louis, Department of Mathematics and Computer Science)

Abstract

The harmonic analysis of the compact circle group T leads in a natural way to the study of the characters of T, the Banach algebra L1(T) and the dual group Z, its characters, and the algebra e1 (Z). All of these structures and their interrelationships are well understood. In another direction, there are a large number of important physical and engineering problems that lead to the formulation of a Sturm-Liouville problem on an interval I, whose eigenfunctions are a useful basis for a weighted L2 space on I. If the Sturm-Liouville operator L, the interval I, and the boundary conditions are appropriate, then the eigenfunctions for the Sturm-Liouville problem will turn out to be the characters of the group T, and the additional algebraic structure in L1(T) becomes available to understand the behavior of expansions in terms of those eigenfunctions/characters.

Suggested Citation

  • W. C. Connett & C. Markett & A. L. Schwartz, 1991. "Jacobi Polynomials and Related Hypergroup Structures," Springer Books, in: Herbert Heyer (ed.), Probability Measures on Groups X, pages 45-81, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2364-6_5
    DOI: 10.1007/978-1-4899-2364-6_5
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