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On a moment problem of analytic functionals of polynomial hypergroups

Shigeru Yamagami

Abstract

Related to radial functions on free groups, we focus on certain polynomial hypergroups and work out spectral analysis with the help of the Stieltjes transform of their analytic functionals.

On a moment problem of analytic functionals of polynomial hypergroups

Abstract

Related to radial functions on free groups, we focus on certain polynomial hypergroups and work out spectral analysis with the help of the Stieltjes transform of their analytic functionals.

Paper Structure

This paper contains 6 sections, 9 theorems, 65 equations, 1 figure.

Table of Contents

  1. Polynomial Hypergroups
  2. Analytic Functionals
  3. Analytic Functionals of Geometric Series
  4. Positive Definite Functions of Haagerup
  5. Off-Spectrum Region
  6. Characterization of Stieltjes Transform

Key Result

Theorem 2.1

An analytic functional $\varphi$ on $\mathscr A$ belongs to $A^*$ if and only if

Figures (1)

  • Figure 1: $\upsilon$-region of C*-boundedness

Theorems & Definitions (23)

  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 2.1
  • Remark 4
  • Remark 5
  • Remark 6
  • Theorem 3.1
  • Remark 7
  • Corollary 3.2: Normalized Limit
  • ...and 13 more