The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Matthias Langer - One of the best experts on this subject based on the ideXlab platform.
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Triple variational principles for self-Adjoint Operator functions
Journal of Functional Analysis, 2016Co-Authors: Matthias Langer, Michael StraussAbstract:For a very general class of unbounded self-Adjoint Operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find conditions which imply that a point is in the resolvent set. For norm resolvent continuous Operator functions we show that the variational inequality becomes an equality.
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the virozub matsaev condition and spectrum of definite type for self Adjoint Operator functions
Complex Analysis and Operator Theory, 2008Co-Authors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-Adjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-Adjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
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The Virozub–Matsaev Condition and Spectrum of Definite Type for Self-Adjoint Operator Functions
Complex Analysis and Operator Theory, 2007Co-Authors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-Adjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-Adjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
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variational principles for eigenvalues of self Adjoint Operator functions
Integral Equations and Operator Theory, 2004Co-Authors: David Eschwe, Matthias LangerAbstract:Variational principles for eigenvalues of certain functions whose values are possibly unbounded self-Adjoint Operators T(λ) are proved. A generalised Rayleigh functional is used that assigns to a vector x a zero of the function T(λ)x, x), where it is assumed that there exists at most one zero. Since there need not exist a zero for all x, an index shift may occur. Using this variational principle, eigenvalues of linear and quadratic polynomials and eigenvalues of block Operator matrices in a gap of the essential spectrum are characterised. Moreover, applications are given to an elliptic eigenvalue problem with degenerate weight, Dirac Operators, strings in a medium with a viscous friction, and a Sturm-Liouville problem that is rational in the eigenvalue parameter.
Heinz Langer - One of the best experts on this subject based on the ideXlab platform.
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the virozub matsaev condition and spectrum of definite type for self Adjoint Operator functions
Complex Analysis and Operator Theory, 2008Co-Authors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-Adjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-Adjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
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The Virozub–Matsaev Condition and Spectrum of Definite Type for Self-Adjoint Operator Functions
Complex Analysis and Operator Theory, 2007Co-Authors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-Adjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-Adjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
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the schur transformation for generalized nevanlinna functions interpolation and self Adjoint Operator realizations
Complex Analysis and Operator Theory, 2007Co-Authors: Daniel Alpay, Heinz Langer, Aad Dijksma, Yuri ShondinAbstract:The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-Adjoint Operator (or relation) realization of a generalized Nevanlinna function.
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self Adjoint analytic Operator functions and their local spectral function
Journal of Functional Analysis, 2006Co-Authors: Heinz Langer, Alexander Markus, Vladimir MatsaevAbstract:For a self-Adjoint analytic Operator function A(λ), which satisfies on some interval Δ of the real axis the Virozub–Matsaev condition, a local spectral function Q on Δ, the values of which are non-negative Operators, is introduced and studied. In the particular case that A(λ)=λI−A with a self-Adjoint Operator A, it coincides with the orthogonal spectral function of A. An essential tool is a linearization of A(λ) by means of a self-Adjoint Operator in some Krein space and the local spectral function of this linearization. The main results of the paper concern properties of the range of Q(Δ) and the description of a natural complement of this range.
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variational principles for real eigenvalues of self Adjoint Operator pencils
Integral Equations and Operator Theory, 2000Co-Authors: Paul Binding, David Eschwe, Heinz LangerAbstract:Double variational principles are established for eigenvalues of a (norm) continuous self-Adjoint Operator valued functionL defined on a real interval [α, β[.L(λ) is not required to be definite for any λ. Applications are made to linear, quadratic and rational functionsL.
George A. Anastassiou - One of the best experts on this subject based on the ideXlab platform.
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Fractional Conformable Self Adjoint Operator Analytic Inequalities
Intelligent Analysis: Fractional Inequalities and Approximations Expanded, 2020Co-Authors: George A. AnastassiouAbstract:We present here conformable fractional self Adjoint Operator comparison, Poincare, Sobolev, Ostrowski and Opial type inequalities. At first we give right and left conformable fractional representation formulae in the self Adjoint Operator sense. Operator inequalities are based in the self Adjoint Operator order over a Hilbert space. See also [3].
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Self Adjoint Operator Korovkin Type Quantitative Approximation Theory
Intelligent Comparisons II: Operator Inequalities and Approximations, 2017Co-Authors: George A. AnastassiouAbstract:Here we present self Adjoint Operator Korovkin type theorems, via self Adjoint Operator Shisha-Mond type inequalities. This is a quantitative treatment to determine the degree of self Adjoint Operator uniform approximation with rates, of sequences of self Adjoint Operator positive linear Operators. We give several applications involving the self Adjoint Operator Bernstein polynomials. It follows [2].
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Self Adjoint Operator Korovkin and Polynomial Direct Approximations with Rates
Intelligent Comparisons II: Operator Inequalities and Approximations, 2017Co-Authors: George A. AnastassiouAbstract:Here we present self Adjoint Operator Korovkin type theorems, via self Adjoint Operator Shisha-Mond type inequalities, also we give self Adjoint Operator polynomial approximations. This is a quantitative treatment to determine the degree of self Adjoint Operator uniform approximation with rates, of sequences of self Adjoint Operator positive linear Operators. The same kind of work is performed over important Operator polynomial sequences. Our approach is direct based on Gelfand isometry. It follows [1].
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Quantitative Self Adjoint Operator Other Direct Approximations
Intelligent Comparisons II: Operator Inequalities and Approximations, 2017Co-Authors: George A. AnastassiouAbstract:Here we give a series of self Adjoint Operator positive linear Operators general results. Then we present specific similar results related to neural networks. This is a quantitative treatment to determine the degree of self Adjoint Operator uniform approximation with rates, of sequences of self Adjoint positive linear Operators in general, and in particular of self Adjoint specific neural network Operators. It follows [4] (Anastassiou, J. Nonlinear Sci. Appl. (2016)).
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Self Adjoint Operator Ostrowski Inequalities
Intelligent Comparisons II: Operator Inequalities and Approximations, 2017Co-Authors: George A. AnastassiouAbstract:We present here several self Adjoint Operator Ostrowski type inequalities to all directions.
Christiane Tretter - One of the best experts on this subject based on the ideXlab platform.
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Bounds on the spectrum and reducing subspaces of a J-self-Adjoint Operator
Indiana University Mathematics Journal, 2010Co-Authors: Sergio Albeverio, Alexander K. Motovilov, Christiane TretterAbstract:Given a self-Adjoint involution J on a Hilbert space H, we consider a J-self-Adjoint Operator L=A+V on H where A is a possibly unbounded self-Adjoint Operator commuting with J and V a bounded J-self-Adjoint Operator anti-commuting with J. We establish optimal estimates on the position of the spectrum of L with respect to the spectrum of A and we obtain norm bounds on the Operator angles between maximal uniformly definite reducing subspaces of the unperturbed Operator A and the perturbed Operator L. All the bounds are given in terms of the norm of V and the distances between pairs of disjoint spectral sets associated with the Operator L and/or the Operator A. As an example, the quantum harmonic oscillator under a PT-symmetric perturbation is discussed. The sharp norm bounds obtained for the Operator angles generalize the celebrated Davis-Kahan trigonometric theorems to the case of J-self-Adjoint perturbations.
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the virozub matsaev condition and spectrum of definite type for self Adjoint Operator functions
Complex Analysis and Operator Theory, 2008Co-Authors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-Adjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-Adjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
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The Virozub–Matsaev Condition and Spectrum of Definite Type for Self-Adjoint Operator Functions
Complex Analysis and Operator Theory, 2007Co-Authors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-Adjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-Adjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
Alexander Markus - One of the best experts on this subject based on the ideXlab platform.
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the virozub matsaev condition and spectrum of definite type for self Adjoint Operator functions
Complex Analysis and Operator Theory, 2008Co-Authors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-Adjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-Adjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
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The Virozub–Matsaev Condition and Spectrum of Definite Type for Self-Adjoint Operator Functions
Complex Analysis and Operator Theory, 2007Co-Authors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-Adjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-Adjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
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self Adjoint analytic Operator functions and their local spectral function
Journal of Functional Analysis, 2006Co-Authors: Heinz Langer, Alexander Markus, Vladimir MatsaevAbstract:For a self-Adjoint analytic Operator function A(λ), which satisfies on some interval Δ of the real axis the Virozub–Matsaev condition, a local spectral function Q on Δ, the values of which are non-negative Operators, is introduced and studied. In the particular case that A(λ)=λI−A with a self-Adjoint Operator A, it coincides with the orthogonal spectral function of A. An essential tool is a linearization of A(λ) by means of a self-Adjoint Operator in some Krein space and the local spectral function of this linearization. The main results of the paper concern properties of the range of Q(Δ) and the description of a natural complement of this range.
