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Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction: Lecture Notes in Mathematics, cartea 1992

Autor Alberto Parmeggiani
en Limba Engleză Paperback – 22 apr 2010
This book grew out of a series of lectures given at the Mathematics Department of Kyushu University in the Fall 2006, within the support of the 21st Century COE Program (2003–2007) “Development of Dynamical Mathematics with High Fu- tionality” (Program Leader: prof. Mitsuhiro Nakao). It was initially published as the Kyushu University COE Lecture Note n- ber 8 (COE Lecture Note, 8. Kyushu University, The 21st Century COE Program “DMHF”, Fukuoka, 2008. vi+234 pp.), and in the present form is an extended v- sion of it (in particular, I have added a section dedicated to the Maslov index). The book is intended as a rapid (though not so straightforward) pseudodiff- ential introduction to the spectral theory of certain systems, mainly of the form a +a where the entries of a are homogeneous polynomials of degree 2 in the 2 0 2 n n (x,?)-variables, (x,?)? R×R,and a is a constant matrix, the so-called non- 0 commutative harmonic oscillators, with particular emphasis on a class of systems introduced by M. Wakayama and myself about ten years ago. The class of n- commutative harmonic oscillators is very rich, and many problems are still open, and worth of being pursued.
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Specificații

ISBN-13: 9783642119217
ISBN-10: 3642119212
Pagini: 272
Ilustrații: XII, 260 p.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.39 kg
Ediția:2010
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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 .

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

One of the main features is the use of techniques that are very powerful and flexible. The approach could be used also for other problems. Another feature constists of an exposition of different results that are scattered throughout the literature. Includes supplementary material: sn.pub/extras