Fractional powers of the operator \(-|x|^2\Delta\) in \(L_p\)-spaces (Q2774462)
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scientific article; zbMATH DE number 1713774
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fractional powers of the operator \(-|x|^2\Delta\) in \(L_p\)-spaces |
scientific article; zbMATH DE number 1713774 |
Statements
2 October 2002
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fractional powers of differential operators
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radial-spherical Fourier multipliers
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Riemann-Liouville functional integrals
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Marchaud's fractional derivatives
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0.92220247
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0.9169603
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0.91148114
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0.90891415
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Fractional powers of the operator \(-|x|^2\Delta\) in \(L_p\)-spaces (English)
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A theory of radial-spherical Fourier multipliers, developed by the reviewer for operators commuting with rotations and dilations in \(R^n\), is applied to constructing fractional powers of the operator \(-|x|^2 \Delta\), where \(\Delta\) denotes the Laplacian in \(R^n\). Fractional powers of this operator are represented as Riemann-Liouville fractional integrals and Marchaud's fractional derivatives associated to the relevant strongly continuous semi-group.
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