To Multidimensional Mellin Analysis: Besov spaces, $K$-functor, approximations, frames
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Accesso online: | |
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| _version_ | 1866914938950254592 |
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| author | Pesenson, Isaac Z. |
| author_facet | Pesenson, Isaac Z. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_07485 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | To Multidimensional Mellin Analysis: Besov spaces, $K$-functor, approximations, frames Pesenson, Isaac Z. Functional Analysis 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. |
| title | To Multidimensional Mellin Analysis: Besov spaces, $K$-functor, approximations, frames |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2207.07485 |