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Windowed Bessel Fourier transform in quantum calculus and applications

机译:窗口贝塞尔傅立叶变换在量子微积分中的应用

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This paper deals firstly with some q-harmonic analysis properties for the q-windowed Bessel Fourier transform related to the q-Bessel function of the third kind as Plancherel formula, inversion formula in . Secondly, we give a weak uncertainty principle for it and we show that the portion of the q-windowed Bessel Fourier transform lying outside some set of finite measure cannot be arbitrarily too small. Then, we verify a version of Heisenberg-Pauli-Weyl type uncertainty inequalities for the q-windowed Bessel Fourier transform and its generalization. Finally, using the kernel reproducing theory, given by Saitoh (Theory of reproducing kernels and its applications. Longman Scientific and Technical, Harlow, 1988), we will be able to realize the natural and powerful approximation problems that lead to the q-windowed Bessel Fourier transform inverses.
机译:本文首先针对与第三类q-贝塞尔函数有关的q窗贝塞尔(Bessel Fourier)变换的一些q调和分析性质,如Plancherel公式,中的反演公式。其次,我们为其给出了一个弱不确定性原理,并且证明了q窗贝塞尔(Bessel Fourier)变换位于某些有限度量集之外的部分不能任意设置得太小。然后,我们验证了q窗Bessel Fourier变换的Heisenberg-Pauli-Weyl型不确定性不等式及其推广。最后,使用Saitoh给出的内核再现理论(再现内核及其应用理论。朗文科学技术,Harlow,1988年),我们将能够实现导致q窗贝塞尔效应的自然且有力的逼近问题傅立叶变换逆。

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