The Fourfold Way in Real Analysis. An Alternative to the Metaplectic Representation (Progress in Mathematics)
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1
The Fourfold Way in Real Analysis An Alternative to the Metaplectic Representation Progress in Mathematics
DE HC NWISBN: 9783764375447 bzw. 3764375442, in Deutsch, Birkhäuser, gebundenes Buch, neu.
Von Händler/Antiquariat, BuySomeBooks [52360437], Las Vegas, NV, U.S.A.
Hardcover. 222 pages. Dimensions: 9.1in. x 6.2in. x 0.7in.The n-dimensionalmetaplectic groupSp(n, R) is the twofoldcoverof the sympl- n n tic group Sp(n, R), which is the group of linear transformations ofX R R that preserve the bilinear (alternate) form x y ( ), ( ) x, y, . (0. 1) 2 n There is a unitary representation of Sp(n, R)intheHilbertspace L (R ), called the metaplectic representation, the image of which is the groupof transformations generated by the following ones: the linear changes of variables, the operators of multiplication by exponentials with pure imaginary quadratic forms in the ex- nent, and the Fourier transformation; some normalization factor enters the de- tion of the operators of the rst and third species. The metaplectic representation was introduced in a great generality in 28 special cases had been considered before, mostly in papers of mathematical physics and it is of such fundamental importancethat the two concepts (the groupand the representation)havebecome virtually indistinguishable. This is not going to be our point of view: indeed, the main point of this work is to show that a certain nite covering of the symplectic group (generally of degree n) has another interesting representation, which enjoys analogues of most of the nicer properties of the metaplectic representation. We shall call it the anaplectic representation other coinages that may come to your mind sound too medical and shall consider rst the one-dimensional case, the main features of which can be described in quite elementary terms. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN.
Hardcover. 222 pages. Dimensions: 9.1in. x 6.2in. x 0.7in.The n-dimensionalmetaplectic groupSp(n, R) is the twofoldcoverof the sympl- n n tic group Sp(n, R), which is the group of linear transformations ofX R R that preserve the bilinear (alternate) form x y ( ), ( ) x, y, . (0. 1) 2 n There is a unitary representation of Sp(n, R)intheHilbertspace L (R ), called the metaplectic representation, the image of which is the groupof transformations generated by the following ones: the linear changes of variables, the operators of multiplication by exponentials with pure imaginary quadratic forms in the ex- nent, and the Fourier transformation; some normalization factor enters the de- tion of the operators of the rst and third species. The metaplectic representation was introduced in a great generality in 28 special cases had been considered before, mostly in papers of mathematical physics and it is of such fundamental importancethat the two concepts (the groupand the representation)havebecome virtually indistinguishable. This is not going to be our point of view: indeed, the main point of this work is to show that a certain nite covering of the symplectic group (generally of degree n) has another interesting representation, which enjoys analogues of most of the nicer properties of the metaplectic representation. We shall call it the anaplectic representation other coinages that may come to your mind sound too medical and shall consider rst the one-dimensional case, the main features of which can be described in quite elementary terms. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN.
2
The Fourfold Way in Real Analysis (2006)
DE HC NWISBN: 9783764375447 bzw. 3764375442, in Deutsch, Springer Basel AG, gebundenes Buch, neu.
Lieferung aus: Deutschland, plus shipping.
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 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. 17.03.2006, gebundene Ausgabe.
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 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. 17.03.2006, gebundene Ausgabe.
3
The Fourfold Way in Real Analysis
~EN HC NWISBN: 9783764375447 bzw. 3764375442, vermutlich in Englisch, Springer Nature, gebundenes Buch, neu.
Lieferung aus: Deutschland, Lagernd, zzgl. Versandkosten.
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. Hard cover.
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. Hard cover.
4
The Fourfold Way in Real Analysis
DE NWISBN: 9783764375447 bzw. 3764375442, in Deutsch, Springer Basel AG, neu.
Lieferung aus: Deutschland, Versandkostenfrei.
Von Händler/Antiquariat, Buchhandlung Kühn GmbH, [4368407].
Neuware - 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. TOC:Introduction.- The One-dimensional Anaplectic Representation.- The n-dimensional Anaplectic Analysis.- Towards the Anaplectic Symbolic Calculi.- The Fourfold Way.- Bibliography.- Index. Buch, Neuware, FixedPrice, 526g.
Von Händler/Antiquariat, Buchhandlung Kühn GmbH, [4368407].
Neuware - 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. TOC:Introduction.- The One-dimensional Anaplectic Representation.- The n-dimensional Anaplectic Analysis.- Towards the Anaplectic Symbolic Calculi.- The Fourfold Way.- Bibliography.- Index. Buch, Neuware, FixedPrice, 526g.
5
The Fourfold Way in Real Analysis
EN USISBN: 9783764375447 bzw. 3764375442, in Englisch, Birkhauser, Birkhauser, Birkhauser, gebraucht.
Lieferung aus: Vereinigte Staaten von Amerika, in-stock.
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.
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.
6
The Fourfold Way in Real Analysis
DE NWISBN: 9783764375447 bzw. 3764375442, in Deutsch, Springer Basel AG, neu.
Lieferung aus: Deutschland, zzgl. Versandkosten, Sofort lieferbar.
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 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.
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 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.
7
The Fourfold Way in Real Analysis (2006)
~EN HC NW FE RPISBN: 9783764375447 bzw. 3764375442, vermutlich in Englisch, 222 Seiten, Birkhaeuser Basel, gebundenes Buch, neu, Erstausgabe, Nachdruck.
Lieferung aus: Deutschland, Versandkosten nach: Deutschland, Versandkostenfrei.
Von Händler/Antiquariat, Moluna GmbH, [5901482].
Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Examines the different, but fully coherent, analysis one could get when trading the usual L2 scalar product for an indefinite oneThe new analysis developed here, 2006, Gebunden, Neuware, Hardcover, 517g, 1. Auflage, 222, Banküberweisung, PayPal.
Von Händler/Antiquariat, Moluna GmbH, [5901482].
Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Examines the different, but fully coherent, analysis one could get when trading the usual L2 scalar product for an indefinite oneThe new analysis developed here, 2006, Gebunden, Neuware, Hardcover, 517g, 1. Auflage, 222, Banküberweisung, PayPal.
8
The Fourfold Way in Real Analysis An Alternative to the Metaplectic Representation (2006)
~EN USISBN: 9783764375447 bzw. 3764375442, vermutlich in Englisch, 2006. Ausgabe, Springer Basel, gebraucht, guter Zustand.
Lieferung aus: Deutschland, Versandkosten nach: Deutschland, Versandkostenfrei.
Von Händler/Antiquariat, Buchpark GmbH, [6065214].
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
Von Händler/Antiquariat, Buchpark GmbH, [6065214].
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
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