Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction

• Main Author: Parmeggiani, Alberto (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Lecture Notes in Mathematics, 1992
• Subjects: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Physics.; Partial Differential Equations.; Global Analysis and Analysis on Manifolds.; Theoretical, Mathematical and Computational Physics.

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...

Table of 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 .