Titlebook: Operator Theory, Analysis and Mathematical Physics; Jan Janas,Pavel Kurasov,Günter Stolz Conference proceedings 2007 Birkh?user Basel 2007

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Uniform and Smooth Benzaid-Lutz Type Theorems and Applications to Jacobi Matrices, generalizations of the Benzaid-Lutz theorem (a Levinson type theorem for discrete linear systems) and are used to develop a technique for proving absence of accumulation points in the pure point spectrum of Jacobi matrices. The technique is illustrated by proving discreteness of the spectrum for a class of unbounded Jacobi operators.

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Operator Theory: Advances and Applicationshttp://image.papertrans.cn/o/image/702344.jpg

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https://doi.org/10.1007/978-3-7643-8135-6Dirichlet-to-Neumann map; Jacobi matrix; Lyapunov exponent; Operator theory; functional model; mathematic

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Finiteness of Eigenvalues of the Perturbed Dirac Operator,Finiteness criteria are established for the point spectrum of the perturbed Dirac operator. The results are obtained by applying the direct methods of the perturbation theory of linear operators. The particular case of the Hamiltonian of a Dirac particle in an electromagnetic field is also considered.

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Trace Formulas for Jacobi Operators in Connection with Scattering Theory for Quasi-Periodic BackgroWe investigate trace formulas for Jacobi operators which are trace class perturbations of quasi-periodic finite-gap operators using Krein’s spectral shift theory. In particular we establish the conserved quantities for the solutions of the Toda hierarchy in this class.

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