Weighted Gelfand pairs, weighted spherical Fourier transform and multipliers
Ass\`ek\`e Y. Tissinam, Abudula\"i Issa, Yaogan Mensah
TL;DR
This paper introduces a generalized Gelfand pair using weighted Lebesgue spaces, constructs associated spherical functions and Fourier transform, and characterizes algebra multipliers through this transform.
Contribution
It extends Gelfand pair theory to weighted settings and develops a new Fourier analysis framework for bi-invariant functions.
Findings
Construction of spherical functions and Fourier transform for weighted Gelfand pairs
Characterization of algebra multipliers via the Fourier transform
Extension of Gelfand pair concepts to weighted Lebesgue spaces
Abstract
A kind of generalized Gelfand pair is introduced via a Banach algebra consisting of bi-invariant functions in a weighted Lebesgue space. The related spherical functions and the Fourier transformation are constructed. The multipliers of the underlying algebra are characterized by this Fourier transformation.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Numerical methods in inverse problems · Spectral Theory in Mathematical Physics