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.

中文翻译：

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广义 Lipschitz 类和 $$q$$ -贝塞尔傅里叶变换的 Boas 和 Titchmarsh 类型定理

摘要

函数\(f\)属于广义 Lipschitz 类\(H^{m,\omega}_{q,\nu}\)和\(h^{m,\omega}_分数\(m\)的{q,\nu}\)根据其\(q\) -贝塞尔-傅里叶变换\(\mathcal F_{q,\nu}(f)\)给出。双重结果也被考虑。分数阶差分的 Titchmarsh 定理的一个类比得到了证明。