scholarly journals Spectral Bounds for Polydiagonal Jacobi Matrix Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Arman Sahovic
Keyword(s):  
Jacobi Matrix ◽  
Symmetric Matrix ◽  
Higher Order ◽  
Main Diagonal ◽  
Matrix Operator ◽  
Discrete Schrödinger Operators ◽  
Canonical Relation ◽  
Spectral Bounds ◽  
Schrödinger Type Operators ◽  
Matrix Operators

The research on spectral inequalities for discrete Schrödinger operators has proved fruitful in the last decade. Indeed, several authors analysed the operator’s canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we consider a generalisation of this relation with regard to connecting higher order Schrödinger-type operators with symmetric matrix operators with arbitrarily many nonzero diagonals above and below the main diagonal. We thus obtain spectral bounds for such matrices, similar in nature to the Lieb-Thirring inequalities.

scholarly journals Riesz Transforms Associated with Higher-Order Schrödinger Type Operators

2017 ◽  
Vol 49 (3) ◽  
pp. 381-410
Author(s):  
Qingquan Deng ◽  
Yong Ding ◽  
Xiaohua Yao
Keyword(s):  
Higher Order ◽  
Riesz Transforms ◽  
Schrödinger Type Operators

scholarly journals Spectral Bounds Using Higher-Order Numerical Ranges

2005 ◽  
Vol 8 ◽  
pp. 17-45 ◽  
Author(s):  
E. B. Davies
Keyword(s):  
Anderson Model ◽  
Adjoint Operator ◽  
Higher Order ◽  
Basic Properties ◽  
Two Space Dimensions ◽  
Spectral Bounds

AbstractThis paper describes how to obtain bounds on the spectrum of a non-self-adjoint operator by means of what are referred to here as ‘its higher-order numerical ranges’. Proofs of some of their basic properties are given, as well as an explanation of how to compute them. Finally, they are used to obtain new spectral insights into the non-self-adjoint Anderson model in one and two space dimensions.

scholarly journals CAPACITIES AND JACOBI MATRICES

2003 ◽  
Vol 46 (3) ◽  
pp. 719-745 ◽  
Author(s):  
Ahmed Sebbar ◽  
Thérèse Falliero
Keyword(s):  
Inverse Problem ◽  
Chebyshev Polynomials ◽  
Jacobi Matrix ◽  
Symmetric Matrix ◽  
Finite Union ◽  
Conformal Mappings ◽  
Subject Classification ◽  
Jacobi Matrices ◽  
Closed Intervals ◽  
Primary 31B15

AbstractIn this paper, we use the theorem of Burchnall and Shaundy to give the capacity of the spectrum $\sigma(A)$ of a periodic tridiagonal and symmetric matrix. A special family of Chebyshev polynomials of $\sigma(A)$ is also given. In addition, the inverse problem is considered: given a finite union $E$ of closed intervals, we study the conditions for a Jacobi matrix $A$ to exist satisfying $\sigma(A)=E$. We relate this question to Carathéodory theorems on conformal mappings.AMS 2000 Mathematics subject classification: Primary 31B15; 30C20; 39A70

BOUNDEDNESS OF ONE CLASS OF THE MATRIX OPERATORS IN WEIG

2020 ◽  
Vol 69 (1) ◽  
pp. 128-133
Author(s):  
А.А. Kalybay ◽  
◽  
А.М. Temirkhanova ◽  
Keyword(s):  
Functional Analysis ◽  
Difference Equation ◽  
Linear Difference Equation ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Matrix Operator ◽  
Classic Problem ◽  
The Matrix ◽  
The Given ◽  
Matrix Operators

Problems of solving different linear difference equation is given to study the properties of the matrix operators in various functional spaces. One of the important problems of functional analysis is to establish criteria of boundedness of the linear operators in functional spaces. Question of the boundedness of matrix operators in sequence spaces is a classic problem of functional analysis and there are many unsolved problems in it. For example, in the general case it is impossible to establish the boundedness of the matrix operator in the spaces of sequences by the given matrix. Therefore, various classes of matrix operators are considered for which the criteria of their boundedness are known. Due to the variety of encountered problems in practice, it is necessary to have various alternative criteria for the boundedness of matrix operators. In this paper, we establish a new alternative criterion for the boundedness of one class of matrix operators.

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