Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction / by Alberto Parmeggiani.

Format:

Book

Author/Creator:

Parmeggiani, Alberto, 1963- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1992.

Lecture Notes in Mathematics, 0075-8434 ; 1992

Language:

English

Subjects (All):

Differential equations, Partial.

Global analysis (Mathematics).

Partial Differential Equations.

Global Analysis and Analysis on Manifolds.

Theoretical, Mathematical and Computational Physics.

Local Subjects:

Partial Differential Equations.

Global Analysis and Analysis on Manifolds.

Theoretical, Mathematical and Computational Physics.

Physical Description:

1 online resource (XII, 260 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.

System Details:

text file PDF

Summary:

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.

Contents:

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 .

Other Format:

Printed edition:

ISBN:

9783642119224

Access Restriction:

Restricted for use by site license.