RKH spaces of Brownian type defined by Cesàro–Hardy operators
| Autor: | Pedro J. Miana, José E. Galé, Luis Sánchez–Lajusticia |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 010102 general mathematics Hilbert space Order (ring theory) Context (language use) Type (model theory) Absolute continuity 01 natural sciences Kernel (algebra) symbols.namesake 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Mathematical Physics Analysis Brownian motion Mathematics Variable (mathematics) |
| Zdroj: | Analysis and Mathematical Physics. 11 |
| ISSN: | 1664-235X 1664-2368 |
| DOI: | 10.1007/s13324-021-00558-5 |
| Popis: | We study reproducing kernel Hilbert spaces introduced as ranges of generalized Cesaro–Hardy operators, in one real variable and in one complex variable. Such spaces can be seen as formed by absolutely continuous functions on the positive half-line (or paths of infinite length) of fractional order, in the real case. A theorem of Paley–Wiener type is given which connects the real setting with the complex one. These spaces are related with fractional operations in the context of integrated Brownian processes. We give estimates of the norms of the corresponding reproducing kernels. |
| Databáze: | OpenAIRE |
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