Distributional fractional powers and Riesz fractional integrals (Q1191656)
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scientific article; zbMATH DE number 60467
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distributional fractional powers and Riesz fractional integrals |
scientific article; zbMATH DE number 60467 |
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Distributional fractional powers and Riesz fractional integrals (English)
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27 September 1992
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In a previous work [Proc. Roy. Soc. Edinburgh, Sect. A 112, No.3/4, 237- 247 (1989; Zbl 0687.47008)], the author developed a fractional power theory for certain operators \(A\) acting on a Fréchet space \(X\), and applied it to Riesz type fractional integrals appearing in the obtention of classical solutions of differential equations. In this paper he derives a fractional power theory for the conjugate operator \(A^*\) from the results for \(A\), and apply it to obtain weak solutions of a Cauchy problem for the three-dimensional wave operator in a half-space.
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fractional power
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Fréchet space
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Riesz type fractional integrals
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conjugate operator
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weak solutions of a Cauchy problem
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three-dimensional wave operator in a half-space
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