Besov and Paley-Wiener spaces, Moduli of continuity and Hardy-Steklov operators associated with the group $"ax+b"$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913215323045888 |
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| author | Pesenson, Isaac |
| author_facet | Pesenson, Isaac |
| contents | We introduce and describe relations between Sobolev, Besov and Paley-Wiener spaces associated with three representations of the Lie group of affine transformations of the line. These representations are left and right regular representations and a representation in a space of functions defined on the half-line. The Besov spaces are described as interpolation spaces between respective Sobolev spaces in terms of the Petree's real interpolation method and in terms of a relevant moduli of continuity. By using a Laplace operators associated with these representations a scales of relevant Paley-Wiener spaces are developed and a corresponding $L_{2}$-approximation theory is constructed in which our Besov spaces appear as approximation spaces. Another description of our Besov spaces is given in terms of a frequency-localized Hilbert frames. A Jackson-type inequalities are also proven. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16734 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Besov and Paley-Wiener spaces, Moduli of continuity and Hardy-Steklov operators associated with the group $"ax+b"$ Pesenson, Isaac Functional Analysis We introduce and describe relations between Sobolev, Besov and Paley-Wiener spaces associated with three representations of the Lie group of affine transformations of the line. These representations are left and right regular representations and a representation in a space of functions defined on the half-line. The Besov spaces are described as interpolation spaces between respective Sobolev spaces in terms of the Petree's real interpolation method and in terms of a relevant moduli of continuity. By using a Laplace operators associated with these representations a scales of relevant Paley-Wiener spaces are developed and a corresponding $L_{2}$-approximation theory is constructed in which our Besov spaces appear as approximation spaces. Another description of our Besov spaces is given in terms of a frequency-localized Hilbert frames. A Jackson-type inequalities are also proven. |
| title | Besov and Paley-Wiener spaces, Moduli of continuity and Hardy-Steklov operators associated with the group $"ax+b"$ |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2401.16734 |