Propagation Properties for Schrödinger Operators Affiliated with Certain C*-Algebras

Amrein, Werner O.; Măntoiu, Marius; Purice, Radu

doi:10.1007/s000230200003

Cited by 25 publications

(46 citation statements)

References 7 publications

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“…Also a simple and transparent proof of the Hunziker, van Winter, Zjislin theorem on the location of essential spectra of multi-particle Hamiltonians was obtained in [32] on the basis of (1). Similar results in the spirit of (1) were derived in [26] by means of admissible geometric methods and in [3,9,10,27] via C * -algebra techniques.…”

Section: Introductionsupporting

confidence: 64%

Fredholm Properties of Band-dominated Operators on Periodic Discrete Structures

Rabinovich

Roch

2008

Complex anal.oper. theory

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Let (X, ∼) be a combinatorial graph the vertex set X of which is a discrete metric space. We suppose that a discrete group G acts freely on (X, ∼) and that the fundamental domain with respect to the action of G contains only a finite set of points. A graph with these properties is called periodic with respect to the group G. We examine the Fredholm property and the essential spectrum of band-dominated operators acting on the spaces l p (X) or c0(X), where (X, ∼) is a periodic graph. Our approach is based on the thorough use of band-dominated operators. It generalizes the necessary and sufficient results obtained in [39] in the special case X = G = Z n and in [42] in case X = G is a general finitely generated discrete group. Mathematics Subject Classification (2000). Primary 47B36; Secondary 47B39, 47A53.

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Section: Introductionsupporting

confidence: 64%

Fredholm Properties of Band-dominated Operators on Periodic Discrete Structures

Rabinovich

Roch

2008

Complex anal.oper. theory

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“…In line with iv), one could also prove some anisotropic non-propagation estimates at suitable energies. More general results of this type can be found in [2].…”

Section: Belongs To B(h)mentioning

confidence: 77%

“…We also rely upon the recent idea that a class of functions defined on IR n having a certain type of anisotropy is associated with a compactification of IR n , the one on which all these functions admit a continuous extension. We refer to [2], [8] and to [12], [13] of M. Mȃntoiu for motivations, for some general principles and in particular for the use of crossed products in relation with spectral analysis. For the scattering theory, the strategy of J. Dereziński and C. Gérard exposed in [4], Sections 6.6 and 6.7, is followed.…”

Section: §1 Introductionmentioning

confidence: 99%

Spectral and Scattering Theory for Schrödinger Operators with Cartesian Anisotropy

Richard¹

2005

Publ. Res. Inst. Math. Sci.

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We study the spectral and scattering theory of some n-dimensional anisotropic Schrödinger operators. The characteristic of the potentials is that they admit limits at infinity separately for each variable. We give a detailed analysis of the spectrum: the essential spectrum, the thresholds, a Mourre estimate, a limiting absorption principle and the absence of singularly continuous spectrum. Then the asymptotic completeness is proved and a precise description of the asymptotic states is obtained in terms of a suitable family of asymptotic operators. §1. IntroductionIn this paper we shall be interested in the spectral and scattering theory of some anisotropic Schrödinger operators H = −∆ + V in the Hilbert space L 2 (IR n ). A general theory for highly anisotropic potentials is still lacking, but various partial approaches are already well developed. The most famous one, and best achieved, is with no doubt the N-body problem (see [16]

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“…(A, V ) prescribed by the behaviour at infinity of B and V . The aims and techniques of proving this result are in a certain relationship with those of [1][2][3][4][5]7] and [11]. Detailed proofs and examples are given in [10].…”

Section: Resultsmentioning

confidence: 96%