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arXiv · 2207.07485

To Multidimensional Mellin Analysis: Besov spaces, $K$-functor, approximations, frames

Isaac Z. Pesenson
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Abstract

In the setting of the multidimensional Mellin analysis we introduce moduli of continuity and use them to define Besov-Mellin spaces. We prove that Besov-Mellin spaces are the interpolation spaces (in the sense of J.Peetre) between two Sobolev-Mellin spaces. We also introduce Bernstein-Mellin spaces and prove corresponding direct and inverse approximation theorems. In the Hilbert case we discuss Laplace-Mellin operaor and define relevant Paley-Wiener-Mellin spaces. Also in the Hilbert case we describe Besov-Mellin spaces in terms of Hilbert frames.

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Isaac Z. Pesenson. 2022-07-15. To Multidimensional Mellin Analysis: Besov spaces, $K$-functor, approximations, frames. https://arxiv.org/abs/2207.07485

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