Spherical Fourier multipliers related to Gelfand pairs
Yaogan Mensah, Marie Fran\c{c}oise Ouedraogo
TL;DR
This paper introduces and analyzes spherical Fourier multipliers on Gelfand pairs, establishing boundedness conditions and Schatten class membership under specific group compactness and summability assumptions.
Contribution
It defines a new class of spherical Fourier multipliers and provides boundedness criteria and Schatten class results, advancing harmonic analysis on Gelfand pairs.
Findings
Established boundedness conditions for spherical Fourier multipliers.
Proved Schatten class membership under compactness and summability assumptions.
Extended harmonic analysis tools for Gelfand pairs.
Abstract
In this paper, we introduce a family of Fourier multipliers using the spherical Fourier transform on Gelfand pairs. We refer to them as spherical Fourier multipliers. We study certain sufficient conditions under which they are bounded. Then, under the hypothesis of compactness of the underlying group and under certain summability conditions, we obtain the belonging of the spherical Fourier multipliers to some Schatten-von Neumann classes.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Algebra and Geometry · Advanced Harmonic Analysis Research