E-Book, Englisch, Band 1992, 260 Seiten, eBook
Reihe: Lecture Notes in Mathematics
Parmeggiani Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction
Erscheinungsjahr 2010
ISBN: 978-3-642-11922-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 1992, 260 Seiten, eBook
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-642-11922-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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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Research
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Weitere Infos & Material
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 .
