Geodesic
The $q$-Fourier transformation of $q$-generalized functions
Sbornik. Mathematics, Tome 190 (1999) no. 5, pp. 717-735 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of functions on the lattice generated by the integer powers of $q^2$, $0. A $q$-analogue of the Fourier transformation is constructed based on the Jackson integral in the space of generalized functions on the lattice. 
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M. A. Olshanetsky; V.-B. K. Rogov. The $q$-Fourier transformation of $q$-generalized functions. Sbornik. Mathematics, Tome 190 (1999) no. 5, pp. 717-735. http://geodesic.mathdoc.fr/item/SM_1999_190_5_a2/

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