Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction / Lecture Notes in Mathematics Bd.1992 (PDF)
(Sprache: Englisch)
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator.
The main technique used is pseudodifferential calculus, including global and semiclassical...
The main technique used is pseudodifferential calculus, including global and semiclassical...
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This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator.
The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of "classical" invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol).
The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of "classical" invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol).
The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Bibliographische Angaben
- Autor: Alberto Parmeggiani
- 2010, 2010, 260 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3642119220
- ISBN-13: 9783642119224
- Erscheinungsdatum: 23.07.2010
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Pressezitat
From the reviews:“The book under review presents the spectral theory of elliptic non-commutative harmonic oscillators, offering also useful information for more general elliptic differential systems. … The book consists of 12 chapters, one appendix and a complete list of references on the subject. … The book addresses important and difficult topics in mathematics. The results are presented in a rigorous, illuminating and elegant way.” (Dumitru Motreanu, Zentralblatt MATH, Vol. 1200, 2011)
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