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Record Nr. |
UNISA996466473303316 |
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Autore |
Führ Hartmut |
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Titolo |
Abstract Harmonic Analysis of Continuous Wavelet Transforms [[electronic resource] /] / by Hartmut Führ |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2005 |
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ISBN |
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Edizione |
[1st ed. 2005.] |
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Descrizione fisica |
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1 online resource (X, 193 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1863 |
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Disciplina |
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Soggetti |
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Harmonic analysis |
Fourier analysis |
Abstract Harmonic Analysis |
Fourier Analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (pages [185]-190) and index. |
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Nota di contenuto |
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Introduction -- Wavelet Transforms and Group Representations -- The Plancherel Transform for Locally Compact Groups -- Plancherel Inversion and Wavelet Transforms -- Admissible Vectors for Group Extension -- Sampling Theorems for the Heisenberg Group -- References -- Index. |
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Sommario/riassunto |
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This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the book can also be read as a problem-driven introduction to the Plancherel formula. |
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