\(a\)-times integrated semigroups and fractional derivation (Q2769468)
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scientific article; zbMATH DE number 1701496
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(a\)-times integrated semigroups and fractional derivation |
scientific article; zbMATH DE number 1701496 |
Statements
6 February 2002
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\(\alpha\)-times integrated semigroups
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functional calculus
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smooth distribution semigroups
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vector-valued Laplace transform
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fractional powers of the infinitesimal generator
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\(a\)-times integrated semigroups and fractional derivation (English)
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The work is devoted to the \(\alpha\)-times integrated semigroups and functional calculus which is related to smooth distribution semigroups. The functional calculus for \(\alpha\)-times integrated semigroups is obtained by applying the fractional integration and derivation to the vector-valued Laplace transform. As application, the fractional powers of the infinitesimal generator, of one \(\alpha\)-times integrated semigroups, are defined.
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