The Fuglede-Putnam theorem and Putnam's inequality for quasi-class (A, k) operators.
Gao, Fugen, Fang, Xiaochun (2011)
Annals of Functional Analysis (AFA) [electronic only]
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Displaying similar documents to “Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians”
The Fuglede-Putnam theorem and Putnam's inequality for quasi-class (A, k) operators.
Absence of eigenvalues for integro-differential operators with periodic coefficients.
Stanescu, Marius Marinel, Cialenco, Igor (2010)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Gelfand transforms of -invariant Schwartz functions on the free group
Véronique Fischer, Fulvio Ricci (2009)
Annales de l’institut Fourier
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The spectrum of a Gelfand pair , where is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz -invariant functions on . We also show the converse in the case of the Gelfand pair , where is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.
Beyond the classical Weyl and Colin de Verdière’s formulas for Schrödinger operators with polynomial magnetic and electric fields
Mitya Boyarchenko, Sergei Levendorski (2006)
Annales de l’institut Fourier
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We present a pair of conjectural formulas that compute the leading term of the spectral asymptotics of a Schrödinger operator on with quasi-homogeneous polynomial magnetic and electric fields. The construction is based on the orbit method due to Kirillov. It makes sense for any nilpotent Lie algebra and is related to the geometry of coadjoint orbits, as well as to the growth properties of certain “algebraic integrals,” studied by Nilsson. By using the direct variational method, we...
Elementary linear algebra for advanced spectral problems
Johannes Sjöstrand, Maciej Zworski (2007)
Annales de l’institut Fourier
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We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators...
On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account.
Zhislin, Grigorii (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to -shifts
Veronica Baker, Marcy Barge, Jaroslaw Kwapisz (2006)
Annales de l’institut Fourier
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This article is devoted to the study of the translation flow on self-similar tilings associated with a substitution of Pisot type. We construct a geometric representation and give necessary and sufficient conditions for the flow to have pure discrete spectrum. As an application we demonstrate that, for certain beta-shifts, the natural extension is naturally isomorphic to a toral automorphism.