Some results on parabolic evolution equations with infinitely many variables (Q1093087)
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scientific article; zbMATH DE number 4021735
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some results on parabolic evolution equations with infinitely many variables |
scientific article; zbMATH DE number 4021735 |
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Some results on parabolic evolution equations with infinitely many variables (English)
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1987
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The author considers the problem (*) \(\Phi_ t=(1/2)Tr(S\Phi_{xx})\), \(\Phi (0,x)=\Phi_ 0(x)\) with S denoting a nuclear positive operator on a separable Hilbert space H, \(\Phi\) being a mapping (0,\(\infty)\times H\to R\) and Tr denoting the trace. Problems of this tpye are of importance in probability theory. The author then proves existence and uniqueness results in problem (*) and extensions of it.
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nuclear positive operator
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separable Hilbert space
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existence
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uniqueness
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