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The Stockwell transform on Gelfand pairs and localization operators

Claude G. Dosseh, Mawoussi Todjro, Yaogan Mensah

Abstract

This paper addresses the extension of the Stockwell transform to Gelfand pairs. Some majors properties of this transform are examined. The localization operators related to the Stockwell transform in this framework are studied.

The Stockwell transform on Gelfand pairs and localization operators

Abstract

This paper addresses the extension of the Stockwell transform to Gelfand pairs. Some majors properties of this transform are examined. The localization operators related to the Stockwell transform in this framework are studied.
Paper Structure (4 sections, 13 theorems, 38 equations)

This paper contains 4 sections, 13 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Harmonic analysis on Gelfand pairs
  3. Stockwell transform on Gelfand pairs
  4. Localization operators related to the Stockwell transform on Gelfand pairs

Key Result

Theorem 2.1

Wolf Let $\varphi$ be a positive-definite function. Then, $\forall x\in G, |\varphi(x)|\leq\varphi(e)$, where $e$ is the neutral element of $G$. $\forall x\in G, \varphi(x^{-1})=\overline{\varphi(x)}$.

Theorems & Definitions (24)

  • Theorem 2.1
  • Theorem 2.2
  • Corollary 2.3
  • Theorem 2.4
  • Definition 3.1
  • Theorem 3.2
  • proof
  • Theorem 3.3
  • proof
  • Definition 3.4
  • ...and 14 more