On convolutions on configuration spaces. I. Spaces of finite configurations
We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space) and study some of their properties. A relationship between the $\ast$-convolution and the convolution of measures on spaces of finite configurations is descri...
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| Datum: | 2012 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2680 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space) and study some of their properties.
A relationship between the $\ast$-convolution and the convolution of measures on spaces of finite configurations is described.
Properties of the operators of multiplication and differentiation with respect to the $\ast$-convolution are investigated.
We also present conditions under which the $\ast$-convolution is positive definite with respect to the $\star$-convolution. |
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