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Record Nr. |
UNINA9910484997303321 |
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Autore |
Parmeggiani Alberto |
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Titolo |
Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction / / by Alberto Parmeggiani |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2010 |
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ISBN |
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Edizione |
[1st ed. 2010.] |
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Descrizione fisica |
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1 online resource (XII, 260 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1992 |
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Disciplina |
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Soggetti |
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Partial differential equations |
Global analysis (Mathematics) |
Manifolds (Mathematics) |
Mathematical physics |
Partial Differential Equations |
Global Analysis and Analysis on Manifolds |
Theoretical, Mathematical and Computational Physics |
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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 and index. |
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Nota di contenuto |
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The Harmonic Oscillator -- The Weyl–Hörmander Calculus -- The Spectral Counting Function N(?) and the Behavior of the Eigenvalues: Part 1 -- The Heat-Semigroup, Functional Calculus and Kernels -- The Spectral Counting Function N(?) and the Behavior of the Eigenvalues: Part 2 -- The Spectral Zeta Function -- Some Properties of the Eigenvalues of -- Some Tools from the Semiclassical Calculus -- On Operators Induced by General Finite-Rank Orthogonal Projections -- Energy-Levels, Dynamics, and the Maslov Index -- Localization and Multiplicity of a Self-Adjoint Elliptic 2×2 Positive NCHO in . |
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Sommario/riassunto |
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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” |
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