Pseudodifferential equations and a generalized translation operator in non-gaussian infinite-dimensional analysis
Pseudodifferential equations of the form $v(D_{\chi})y = f$ (where $v$ is a function holomorphic at zero and $D_{\chi}$ is a pseudodifferential operator) are studied on spaces of test functions of non-Gaussian infinite-dimensional analysis. The results obtained are applied to construct a generalize...
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| Datum: | 1999 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1999
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4732 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Pseudodifferential equations of the form $v(D_{\chi})y = f$ (where $v$ is a function holomorphic at zero and $D_{\chi}$ is a pseudodifferential operator)
are studied on spaces of test functions of non-Gaussian infinite-dimensional analysis. The results obtained are applied to construct a generalized
translation operator $T^{\chi}_y = \chi(\langle y, D_{\chi}\rangle)$ the already mentioned spaces and to study its properties.
In particular, the associativity, the commutativity, and another properties of $T^{\chi}_y$ which are analogs of the classical properties of a generalized translation operator. |
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