On the Wiener semigroup and harmonic analysis on the infinite dimensional torus (Q1110746)
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scientific article; zbMATH DE number 4073628
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Wiener semigroup and harmonic analysis on the infinite dimensional torus |
scientific article; zbMATH DE number 4073628 |
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On the Wiener semigroup and harmonic analysis on the infinite dimensional torus (English)
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1987
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We present a model for which certain difficulties often associated with analysis on infinite-dimensional spaces do not occur. In this situation, the convolution semigroup of Wiener measures constructed by Gross becomes a self-adjoint contraction semigroup. We generalize a facet of Sobolev theory to our infinite-dimensional context, and consider the differentiability of Wiener measure in this new weak sense.
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infinite-dimensional analysis
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Wiener measure
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partial differential equations
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analysis on infinite-dimensional spaces
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convolution semigroup
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Wiener measures
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self-adjoint contraction semigroup
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differentiability of Wiener measure
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