The $q$-Fourier transform of $q$-distributions

Abstract

We consider functions on the lattice generated by the integer powers of $q^2$ for $0<q<1$ and construct the $q$-analog of Fourier transform based on the Jackson integral in the space of distributions on the lattice.

arXiv comment18 pages, latex, typos corrected, added references

References in corpus (3)

• Algebraic {$q$}-Integration and Fourier Theory on Quantum and Braided Spaces
• Special functions and q-commuting variables
• On a general q-Fourier transformation with nonsymmetric kernels

Cited by in corpus (2)

• On the braided Fourier transform in the n-dimensional quantum space
• q-convolution and its q-Fourier transform