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100   $a20100721d2010      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aSpectral Theory of Non-Commutative Harmonic Oscillators: An Introduction /$fby Alberto Parmeggiani
205   $a1st ed. 2010.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2010.
215   $a1 online resource (XII, 260 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1992
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-11921-2 
320   $aIncludes bibliographical references and index.
327   $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 .
330   $aThis volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of ?classical? invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1992
606   $aPartial differential equations
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aMathematical physics
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082
606   $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005
615  0$aPartial differential equations.
615  0$aGlobal analysis (Mathematics).
615  0$aManifolds (Mathematics).
615  0$aMathematical physics.
615 14$aPartial Differential Equations.
615 24$aGlobal Analysis and Analysis on Manifolds.
615 24$aTheoretical, Mathematical and Computational Physics.
676   $a515.353
700   $aParmeggiani$b Alberto$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478937
906   $aBOOK
912   $a9910484997303321
996   $aSpectral theory of non-commutative harmonic oscillators$9261790
997   $aUNINA