Geodesic
Boas and Titchmarsh Type Theorems for Generalized Lipschitz Classes and $q$-Bessel Fourier Transform
Matematičeskie zametki, Tome 114 (2023) no. 1, pp. 68-80

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Necessary and sufficient conditions for a function $f$ to belong to the generalized Lipschitz classes $H^{m,\omega}_{q,\nu}$ and $h^{m,\omega}_{q,\nu}$ for fractional $m$ are given in terms of its $q$-Bessel–Fourier transform $\mathcal F_{q,\nu}(f)$. Dual results are considered as well. An analog of the Titchmarsh theorem for fractional-order differences is proved.
Keywords: generalized Lipschitz class
Mots-clés : Fourier transform, $q$-Bessel–Fourier transform. 
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     author = {S. S. Volosivets and Yu. I. Krotova},
     title = {Boas and {Titchmarsh} {Type} {Theorems} for {Generalized} {Lipschitz} {Classes} and $q${-Bessel} {Fourier} {Transform}},
     journal = {Matemati\v{c}eskie zametki},
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S. S. Volosivets; Yu. I. Krotova. Boas and Titchmarsh Type Theorems for Generalized Lipschitz Classes and $q$-Bessel Fourier Transform. Matematičeskie zametki, Tome 114 (2023) no. 1, pp. 68-80. http://geodesic.mathdoc.fr/item/MZM_2023_114_1_a4/