Sampling in reproducing kernel Banach spaces on Lie groups
| Autor: | Jens Gerlach Christensen |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Mathematics(all)
General Mathematics Poisson kernel Banach space 010103 numerical & computational mathematics 01 natural sciences symbols.namesake Polynomial kernel FOS: Mathematics 0101 mathematics Sampling Bergman kernel Mathematics Numerical Analysis Lie groups Representer theorem Applied Mathematics 010102 general mathematics Reproducing kernel Banach spaces Coorbits Functional Analysis (math.FA) Mathematics - Functional Analysis Algebra Kernel embedding of distributions Kernel (statistics) symbols 43A15 46E15 94A12 Analysis Reproducing kernel Hilbert space |
| Zdroj: | Journal of Approximation Theory. 164:179-203 |
| ISSN: | 0021-9045 |
| DOI: | 10.1016/j.jat.2011.10.002 |
| Popis: | We present sampling theorems for reproducing kernel Banach spaces on Lie groups. Recent approaches to this problem rely on integrability of the kernel and its local oscillations. In this paper, we replace these integrability conditions by requirements on the derivatives of the reproducing kernel and, in particular, oscillation estimates are found using derivatives of the reproducing kernel. This provides a convenient path to sampling results on reproducing kernel Banach spaces. Finally, these results are used to obtain frames and atomic decompositions for Banach spaces of distributions stemming from a cyclic representation. It is shown that this process is particularly easy, when the cyclic vector is a Gårding vector for a square integrable representation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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