Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913276640624640 |
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| author | Hovemann, Marc |
| author_facet | Hovemann, Marc |
| contents | In this paper we deduce new characterizations for bivariate Bessel-Potential spaces defined on the unit square via B-spline quarklets. For that purpose in a first step we use univariate boundary adapted quarklets to describe univariate Bessel-Potential spaces on intervals. To obtain the bivariate characterizations a recent result of Hansen and Sickel is applied. It yields that each bivariate Bessel-Potential space on a square can be written as an intersection of function spaces which have a tensor product structure. Hence our main result is a characterization of bivariate Bessel-Potential spaces on squares in terms of quarklets that are tensor products of univariate quarklets on intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products Hovemann, Marc Functional Analysis Analysis of PDEs 46E35 In this paper we deduce new characterizations for bivariate Bessel-Potential spaces defined on the unit square via B-spline quarklets. For that purpose in a first step we use univariate boundary adapted quarklets to describe univariate Bessel-Potential spaces on intervals. To obtain the bivariate characterizations a recent result of Hansen and Sickel is applied. It yields that each bivariate Bessel-Potential space on a square can be written as an intersection of function spaces which have a tensor product structure. Hence our main result is a characterization of bivariate Bessel-Potential spaces on squares in terms of quarklets that are tensor products of univariate quarklets on intervals. |
| title | Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products |
| topic | Functional Analysis Analysis of PDEs 46E35 |
| url | https://arxiv.org/abs/2403.14388 |