2018
Том 70
№ 5

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Pseudodifferential equations and a generalized translation operator in non-gaussian infinite-dimensional analysis

Kachanovskii N. A.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 10, pp 1503-1511.

Citation Example: Kachanovskii N. A. Pseudodifferential equations and a generalized translation operator in non-gaussian infinite-dimensional analysis // Ukr. Mat. Zh. - 1999. - 51, № 10. - pp. 1334–1341.

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