[PDF] Top 20 Sum rules and the Szego condition for Jacobi matrices
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Sum rules and the Szego condition for Jacobi matrices
... Although Jacobi matrices and orthogonal polynomials have a lot in common, it seems that there has not been much interaction between these two ...the sum rules for Jacobi ... See full document
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Sum rules for Jacobi matrices and their applications to spectral theory
... The sum rule: Second proof In this section, we will provide a second proof of the sum rules that never mentions a perturbation determinant or a Jost function ... See full document
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Spectral properties of Jacobi matrices and sum rules of special form
... The article is organized in the following way. Preliminary facts are listed in Section 1. A method of deriving the sum rules on ¯ C \[−2, 2] is explained in Section 2. Theorem 3 is proved in Section 3, the ... See full document
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Sum Rules and the Szegő Condition for Orthogonal Polynomials on the Real Line
... arXiv:math-ph/0206023v1 14 Jun 2002 ORTHOGONAL POLYNOMIALS ON THE REAL LINE BARRY SIMON 1 AND ANDREJ ZLATOˇ S Abstract. We study the Case sum rules, especially C 0 , for gen- eral Jacobi ... See full document
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Finite Gap Jacobi Matrices, II. The Szegő Class
... As noted in the introduction, a key to the approach to Szeg˝o-type theorems for e = [ −2, 2] that we’ll follow is step-by-step sum rules. Our goal in this section is to prove those for a general finite gap ... See full document
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Jacobi matrices and quadrature rules on the unit circle and the real line
... An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff system and DAEs. Part I[r] ... See full document
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CiteSeerX — Sum rules and the Szegő condition for orthogonal polynomials on the real line
... these sum rules as a spe tral tool (motivated in turn by work on S hr odinger operators by Deift-Killip [4℄ and Denissov ...proving sum rules on as large a lass of J 's as ... See full document
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Block-oriented J-Jacobi methods for Hermitian matrices
... the condition number of | R r | , is not larger than n times the condition number of | R c | , where R r = Δ r R ( R c = R Δ c ) and Δ r ( Δ c ) is so chosen that the rows of R r (columns of R c ) have unit ... See full document
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Spectral representations for a class of banded Jacobi-type matrices
... (i) for each λ ∈ Γ, the space E(λ)H is invariant for A, (ii) for each λ ∈ Γ, σ(AE(λ)) = {µ ∈ Γ : µ ≺ λ} and σ(A(I − E(λ))) = {µ ∈ Γ : λ ≺ µ}. The latter can be regarded as the separability condition of the ... See full document
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An inverse eigenvalue problem for periodic Jacobi matrices in Minkowski spaces
... In Section 2, we give a necessary and sufficient condition for the existence of a solution of PJI, and also a necessary and sufficient condition ensuring uniqueness of the solution. In Section 3, an ... See full document
13
Random block matrices generalizing the classical Jacobi and Laguerre ensembles
... that condition (4.13) ensures the existence of the limiting matrices C ( p ) ( s ) and D ( p ) ( s ) ...The condition can be relaxed for some j, as long as the limits of the matrix entries still ... See full document
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Integral Representations for Spectral Functions of Some Nonself-Adjoint Jacobi Matrices
... C N + = {λ ∈ C : |λ − c + | = N, Im λ ≥ r 1 + ε}, C N − = {λ ∈ C : |λ − c − | = N, Im λ ≤ r 0 − ε}. Condition (54) ensures that the points a + N , c + , b + N and the half of the circle, C N + , lie in the open ... See full document
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Unbounded Jacobi matrices at critical coupling
... Available online 23 October 2007 Abstract We consider a class of Jacobi matrices with unbounded coefficients. This class is known to exhibit a first-order phase transition in the sense that, as a parameter is ... See full document
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Spectral problems for generalized Jacobi matrices
... Abstract A new class of generalized Jacobi matrices is introduced. Every proper real rational func- tion is proved to be the m-function of a unique finite generalized Jacobi matrix. Moreover, every ... See full document
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Asymptotics of the discrete spectrum for complex Jacobi matrices
... tridiagonal matrices and complex Jacobi ma- trices are investigated by several authors: Beckermann and Kaliaguine ([1, 2]), Djakov and Mityagin ([7, 8]), Egorova and Golinskii ([10, 11]) and others (see, ... See full document
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Mourre's theory for some unbounded Jacobi matrices
... of Jacobi matrices we refer the reader to [2] (see also [16] for recent ...of Jacobi matrices are extensively studied by the help of different methods, see for example [5–15,17,19] and ... See full document
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On the measure of the absolutely continuous spectrum for Jacobi matrices
... Available online 21 December 2010 Communicated by Serguei Denissov Abstract We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support Σ ac of the absolutely ... See full document
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Inverse problems for periodic generalized Jacobi matrices
... Keywords: Generalized Jacobi matrix Periodic continued fraction Inverse problem Pell–Abel equation J -unitary matrix polynomial Monodromy matrix.. Introduction In 1826, Abel proved that [r] ... See full document
9
Spectral theory of certain unbounded Jacobi matrices
... • In Appendix A we consider some special cases where one has simple commutation rules and so Mourre’s method gives more than what we obtain in the general case and in a quite elegant manner. 2. Elementary analysis ... See full document
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The Jacobi matrices approach to Nevanlinna–Pick problems
... Abstract A modification of the well-known step-by-step process for solving Nevanlinna–Pick problems in the class of R 0 -functions gives rise to a linear pencil H −λJ, where H and J are Hermitian tridiagonal ... See full document
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