The $q$-Fourier transform of $q$-distributions
M.Olshanetsky, V.Rogov
TL;DR
This paper introduces a $q$-analog of the Fourier transform for functions on a lattice generated by powers of $q^2$, utilizing the Jackson integral within the distribution space.
Contribution
It constructs a novel $q$-Fourier transform based on Jackson integral, extending Fourier analysis to $q$-distributions on a lattice.
Findings
Defined the $q$-Fourier transform on the lattice
Established properties of the $q$-transform in distribution space
Provided a framework for $q$-analogs of classical Fourier analysis
Abstract
We consider functions on the lattice generated by the integer powers of for and construct the -analog of Fourier transform based on the Jackson integral in the space of distributions on the lattice.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical functions and polynomials · Advanced Harmonic Analysis Research