This article is cited in 5 papers

The $q$-Fourier transformation of $q$-generalized functions

M. A. Olshanetsky^a, V.-B. K. Rogov<sup>b

a</sup> Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
^b Moscow State University of Railway Communications

Abstract: A study is made of functions on the lattice generated by the integer powers of $q^2$, $0<q<1$. A $q$-analogue of the Fourier transformation is constructed based on the Jackson integral in the space of generalized functions on the lattice.

UDC: 517.58

MSC: Primary 42A38, 46F05; Secondary 81R50, 17B37, 81S05

Received: 03.02.1998

DOI: 10.4213/sm403

 English version: Sbornik: Mathematics, 1999, 190:5, 717–735

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