000 03401nam a22004815i 4500
001 978-3-642-11922-4
003 DE-He213
005 20190213151358.0
007 cr nn 008mamaa
008 100721s2010 gw | s |||| 0|eng d
020 _a9783642119224
_9978-3-642-11922-4
024 7 _a10.1007/978-3-642-11922-4
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.353
_223
100 1 _aParmeggiani, Alberto.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSpectral Theory of Non-Commutative Harmonic Oscillators: An Introduction
_h[electronic resource] /
_cby Alberto Parmeggiani.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXII, 260 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1992
505 0 _aThe 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 .
520 _aThis 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.
650 0 _aDifferential equations, partial.
650 0 _aGlobal analysis.
650 1 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642119217
776 0 8 _iPrinted edition:
_z9783642119231
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1992
856 4 0 _uhttps://doi.org/10.1007/978-3-642-11922-4
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10470
_d10470