Displaying similar documents to “A Weyl-Titchmarsh type formula for a discrete Schrödinger operator with Wigner-von Neumann potential”

On a Weyl-von Neumann type theorem for antilinear self-adjoint operators

Santtu Ruotsalainen (2012)

Studia Mathematica

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Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators...

On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation

François Castella (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann...

On the Neumann problem with combined nonlinearities

Jan Chabrowski, Jianfu Yang (2005)

Annales Polonici Mathematici

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We establish the existence of multiple solutions of an asymptotically linear Neumann problem. These solutions are obtained via the mountain-pass principle and a local minimization.

Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher

Michael Skeide (2006)

Banach Center Publications

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The category of von Neumann correspondences from 𝓑 to 𝓒 (or von Neumann 𝓑-𝓒-modules) is dual to the category of von Neumann correspondences from 𝓒' to 𝓑' via a functor that generalizes naturally the functor that sends a von Neumann algebra to its commutant and back. We show that under this duality, called commutant, Rieffel's Eilenberg-Watts theorem (on functors between the categories of representations of two von Neumann algebras) switches into Blecher's Eilenberg-Watts theorem...

On Woronowicz's approach to the Tomita-Takesaki theory

László Zsidó (2012)

Banach Center Publications

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The Tomita-Takesaki Theory is very complex and can be contemplated from different points of view. In the decade 1970-1980 several approaches to it appeared, each one seeking to attain more transparency. One of them was the paper of S. L. Woronowicz "Operator systems and their application to the Tomita-Takesaki theory" that appeared in 1979. Woronowicz's approach allows a particularly precise insight into the nature of the Tomita-Takesaki Theory and in this paper we present a brief, but...

On spectral problems of discrete Schrödinger operators

Chi-Hua Chan, Po-Chun Huang (2021)

Applications of Mathematics

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A special type of Jacobi matrices, discrete Schrödinger operators, is found to play an important role in quantum physics. In this paper, we show that given the spectrum of a discrete Schrödinger operator and the spectrum of the operator obtained by deleting the first row and the first column of it can determine the discrete Schrödinger operator uniquely, even though one eigenvalue of the latter is missing. Moreover, we find the forms of the discrete Schrödinger operators when their smallest...

On the Neumann problem with L¹ data

J. Chabrowski (2007)

Colloquium Mathematicae

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We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.