Spectral theory of non-commutative harmonic oscillators : an introduction

書誌事項

Spectral theory of non-commutative harmonic oscillators : an introduction

Alberto Parmeggiani

(Lecture notes in mathematics, 1992)

Springer, c2010

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注記

Bibliography: p. 249-251

Includes index

内容説明・目次

内容説明

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,?)? RxR,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.

目次

The Harmonic Oscillator.- The Weyl-Hoermander 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 2x2 Positive NCHO in .

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詳細情報

  • NII書誌ID(NCID)
    BB02247093
  • ISBN
    • 9783642119217
  • LCCN
    2010924182
  • 出版国コード
    gw
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Berlin
  • ページ数/冊数
    xi, 254 p.
  • 大きさ
    24 cm
  • 件名
  • 親書誌ID
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