Convolution, Fourier analysis, and distributions generated by Riesz bases
Michael Ruzhansky, Niyaz Tokmagambetov
TL;DR
This paper explores convolution operations, Fourier analysis, and distribution theory derived from Riesz bases in Hilbert spaces, providing foundational insights and examples for advanced functional analysis.
Contribution
It introduces a framework for convolutions and Fourier analysis based on biorthogonal systems of Riesz bases, expanding the theoretical tools available in Hilbert space analysis.
Findings
Developed convolution notions from Riesz bases
Established biorthogonal Fourier analysis framework
Provided examples illustrating the theory
Abstract
In this note we discuss notions of convolutions generated by biorthogonal systems of elements of a Hilbert space. We develop the associated biorthogonal Fourier analysis and the theory of distributions, discuss properties of convolutions and give a number of examples.
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