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 eigenvalues 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.

Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction

PARMEGGIANI, ALBERTO
2010

Abstract

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 eigenvalues 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.
272
9783642119217
A. Parmeggiani
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/89216
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 5
social impact