Bound states and scattered states for contraction semigroups (Q792601)
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scientific article; zbMATH DE number 3853827
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bound states and scattered states for contraction semigroups |
scientific article; zbMATH DE number 3853827 |
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Bound states and scattered states for contraction semigroups (English)
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1985
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Let A generate a strongly continuous contraction semigroup T(t) on a Hilbert space. If \(L(\zeta I-A)^{-1}\) is compact, then the Cesàro limit of \(\| LT(t)f\|^ 2\) (as \(t\to \infty)\) is computed for all vectors f. This limit is interpreted in terms of bound and scattered states in the context of quantum mechanical and classical wave propagation problems.
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asymptotics
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RAGE theorem
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mean ergodic theorem
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Wiener's theorem
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almost convergence
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strongly continuous contraction semigroup
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Cesàro limit
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bound and scattered states
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quantum mechanical and classical wave propagation problems
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0.86064297
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0.8591751
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0.8545559
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