Weyl-Titchmarsh type formula for Hermite operator with small perturbation
نویسندگان
چکیده
منابع مشابه
Weyl-titchmarsh Type Formula for Hermite Operator with Small Perturbation
Small perturbations of the Jacobi matrix with weights √ n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical Weyl-Titchmarsh formula for the Schrödinger operator on the half-line with summable potential. Additionally a base of generalized eigenvectors for ”free” Hermite ope...
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In this work, we establish Weyl–Titchmarsh theory for symplectic difference systems. This paper extends classical Weyl–Titchmarsh theory and provides a foundation for studying spectral theory of symplectic difference systems. 2010 Elsevier Inc. All rights reserved.
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and Applied Analysis 3 and spectral theory for the system 1.2 . Shi studied Weyl-Titchmarsh theory and spectral theory for the system 1.2 in 33, 34 ; Clark and Gesztesy established the Weyl-Titchmarsh theory for a class of discrete Hamiltonian systems that include system 1.2 23 . Sun et al. established the GKN-theory for the system 1.2 35 . 1.3. Dynamic Equations A time scale T is an arbitrary ...
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We develop Weyl–Titchmarsh theory for Schrödinger operators with strongly singular potentials such as perturbed spherical Schrödinger operators (also known as Bessel operators). It is known that in such situations one can still define a corresponding singular Weyl m-function and it was recently shown that there is also an associated spectral transformation. Here we will give a general criterion...
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We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh matrixvalued functions as well as a new version of the functional model in such realizations are presented. In the case of periodic Herglotz-Nevanlinna matrix-v...
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ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2009
ISSN: 1232-9274
DOI: 10.7494/opmath.2009.29.2.187