Operator theory and harmonic analysis (Q2772767)
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scientific article; zbMATH DE number 1708208
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Operator theory and harmonic analysis |
scientific article; zbMATH DE number 1708208 |
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1 April 2003
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operator theory
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harmonic analysis
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spectral theorem
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unitary operators
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isometries
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isometric lifting
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unitary dilation
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commutant lifting
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Operator theory and harmonic analysis (English)
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A deep survey paper describing the relations between operator theory and harmonic analysis in the light of the recent decades. Special attention is paid to the following subjects: (a) the spectral theorem for unitary operators in the spirit of the Herglotz-F.Riesz-Toeplitz theorem, (b) the structure of isometries as underlined by the Wold-von Neumann-Kolmogorov theorem with application to Beurling's invariant subspace theorem, (c) isometric lifting and unitary dilation of constructive operators as developed by B. Sz. Nagy, (d) the commutant lifting theorem with applications to problems of interpolation.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00019].
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