The fourfold way in real analysis: an alternative to the metaplectic representation
The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be given a...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2006
|
| Schriftenreihe: | Progress in mathematics
250 |
| Schlagworte: | |
| Zusammenfassung: | The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be given a parameter-dependent analogue. The parameter is some real number modulo 2, the classical case being obtained when it is an integer. The space L2(R) has to give way to a pseudo-Hilbert space, on which a new translation-invariant integral still exists. All this extends to the n-dimensional case, and in the alternative to the metaplectic representation so obtained, it is the space of Lagrangian subspaces of R2n that plays the usual role of the complex Siegel domain. In fourfold analysis, the spectrum of the harmonic oscillator can be an arbitrary class modulo the integers. Even though the whole development touches upon notions of representation theory, pseudodifferential operator theory, and algebraic geometry, it remains completely elementary in all these aspects. The book should be of interest to researchers working in analysis in general, in harmonic analysis, or in mathematical physics. |
| Beschreibung: | X, 220 S. |
| ISBN: | 3764375442 9783764375447 |
Internformat
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| 490 | 1 | |a Progress in mathematics |v 250 | |
| 520 | 3 | |a The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be given a parameter-dependent analogue. The parameter is some real number modulo 2, the classical case being obtained when it is an integer. The space L2(R) has to give way to a pseudo-Hilbert space, on which a new translation-invariant integral still exists. All this extends to the n-dimensional case, and in the alternative to the metaplectic representation so obtained, it is the space of Lagrangian subspaces of R2n that plays the usual role of the complex Siegel domain. In fourfold analysis, the spectrum of the harmonic oscillator can be an arbitrary class modulo the integers. Even though the whole development touches upon notions of representation theory, pseudodifferential operator theory, and algebraic geometry, it remains completely elementary in all these aspects. The book should be of interest to researchers working in analysis in general, in harmonic analysis, or in mathematical physics. | |
| 650 | 4 | |a Analyse harmonique | |
| 650 | 4 | |a Espace des phases (Physique statistique) | |
| 650 | 4 | |a Espaces à produit scalaire | |
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| 650 | 4 | |a Lie, Groupes de | |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
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| discipline | Mathematik |
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| id | DE-604.BV021294931 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:50:56Z |
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| institution | BVB |
| isbn | 3764375442 9783764375447 |
| language | English |
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| physical | X, 220 S. |
| publishDate | 2006 |
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| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Unterberger, André 1940- Verfasser (DE-588)122184882 aut The fourfold way in real analysis an alternative to the metaplectic representation André Unterberger Basel [u.a.] Birkhäuser 2006 X, 220 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 250 The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be given a parameter-dependent analogue. The parameter is some real number modulo 2, the classical case being obtained when it is an integer. The space L2(R) has to give way to a pseudo-Hilbert space, on which a new translation-invariant integral still exists. All this extends to the n-dimensional case, and in the alternative to the metaplectic representation so obtained, it is the space of Lagrangian subspaces of R2n that plays the usual role of the complex Siegel domain. In fourfold analysis, the spectrum of the harmonic oscillator can be an arbitrary class modulo the integers. Even though the whole development touches upon notions of representation theory, pseudodifferential operator theory, and algebraic geometry, it remains completely elementary in all these aspects. The book should be of interest to researchers working in analysis in general, in harmonic analysis, or in mathematical physics. Analyse harmonique Espace des phases (Physique statistique) Espaces à produit scalaire Fourier, Analyse de Lie, Groupes de Fourier analysis Harmonic analysis Inner product spaces Lie groups Phase space (Statistical physics) Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Metaplektische Darstellung (DE-588)4204500-9 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Reelle Analysis (DE-588)4627581-2 s Metaplektische Darstellung (DE-588)4204500-9 s 1\p DE-604 Progress in mathematics 250 (DE-604)BV000004120 250 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Unterberger, André 1940- The fourfold way in real analysis an alternative to the metaplectic representation Progress in mathematics Analyse harmonique Espace des phases (Physique statistique) Espaces à produit scalaire Fourier, Analyse de Lie, Groupes de Fourier analysis Harmonic analysis Inner product spaces Lie groups Phase space (Statistical physics) Harmonische Analyse (DE-588)4023453-8 gnd Metaplektische Darstellung (DE-588)4204500-9 gnd Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4204500-9 (DE-588)4627581-2 |
| title | The fourfold way in real analysis an alternative to the metaplectic representation |
| title_auth | The fourfold way in real analysis an alternative to the metaplectic representation |
| title_exact_search | The fourfold way in real analysis an alternative to the metaplectic representation |
| title_exact_search_txtP | The fourfold way in real analysis an alternative to the metaplectic representation |
| title_full | The fourfold way in real analysis an alternative to the metaplectic representation André Unterberger |
| title_fullStr | The fourfold way in real analysis an alternative to the metaplectic representation André Unterberger |
| title_full_unstemmed | The fourfold way in real analysis an alternative to the metaplectic representation André Unterberger |
| title_short | The fourfold way in real analysis |
| title_sort | the fourfold way in real analysis an alternative to the metaplectic representation |
| title_sub | an alternative to the metaplectic representation |
| topic | Analyse harmonique Espace des phases (Physique statistique) Espaces à produit scalaire Fourier, Analyse de Lie, Groupes de Fourier analysis Harmonic analysis Inner product spaces Lie groups Phase space (Statistical physics) Harmonische Analyse (DE-588)4023453-8 gnd Metaplektische Darstellung (DE-588)4204500-9 gnd Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Analyse harmonique Espace des phases (Physique statistique) Espaces à produit scalaire Fourier, Analyse de Lie, Groupes de Fourier analysis Harmonic analysis Inner product spaces Lie groups Phase space (Statistical physics) Harmonische Analyse Metaplektische Darstellung Reelle Analysis |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT unterbergerandre thefourfoldwayinrealanalysisanalternativetothemetaplecticrepresentation |