Abstract
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.
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Acknowledgments
We express our gratitude to the referee for valuable remarks, which have helped us to improve the exposition.
Funding
The first author’s research was supported by the Development Program of the Regional Scientific-Educational Center “Mathematics for Future Technology” (project no. 075-02-2023-949).
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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 68–80 https://doi.org/10.4213/mzm13467.
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Volosivets, S.S., Krotova, Y.I. Boas and Titchmarsh Type Theorems for Generalized Lipschitz Classes and \(q\)-Bessel Fourier Transform. Math Notes 114, 55–65 (2023). https://doi.org/10.1134/S0001434623070052
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DOI: https://doi.org/10.1134/S0001434623070052