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Approximation results for reflectionless Jacobi matrices [PDF]
International Mathematics Research Notices, 2010 We study spaces of reflectionless Jacobi matrices. The main theme is the following type of question: Given a reflectionless Jacobi matrix, is it possible to approximate it by other reflectionless and, typically, simpler Jacobi matrices of a special type?
Poltoratski, Alexei, Remling, Christian
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Localization of Discrete Time Quantum Walks on the Glued Trees [PDF]
Entropy, 2014 In this paper, we consider the time averaged distribution of discrete time quantum walks on the glued trees. In order to analyze the walks on the glued trees, we consider a reduction to the walks on path graphs.
Yusuke Ide +3 more
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A note on reflectionless Jacobi matrices [PDF]
Communications in Mathematical Physics, 2013 The property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl m-functions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a characterization in
Jaksic, Vojkan +2 more
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Ergodic Jacobi matrices and conformal maps [PDF]
Mathematical Physics, Analysis and Geometry, 2011 We study structural properties of the Lyapunov exponent $\gamma$ and the density of states $k$ for ergodic (or just invariant) Jacobi matrices in a general framework.
A Avila +31 more
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Deficiency Indices of Block Jacobi Matrices: Survey
Современная математика: Фундаментальные направления, 2021 The paper is a survey and concerns with infinite symmetric block Jacobi matrices J with m×m-matrix entries. We discuss several results on general block Jacobi matrices to be either self-adjoint or have maximal as well as intermediate deficiency indices ...
Viktoriya S. Budyka +2 more
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Analysis of RL electric circuits modeled by fractional Riccati IVP via Jacobi-Broyden Newton algorithm. [PDF]
PLoS ONEThis paper focuses on modeling Resistor-Inductor (RL) electric circuits using a fractional Riccati initial value problem (IVP) framework. Conventional models frequently neglect the complex dynamics and memory effects intrinsic to actual RL circuits. This
Mahmoud Abd El-Hady +3 more
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Fractal and Fractional, 2023 This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as the collocation points and derived the ...
Zhongshu Wu +3 more
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Spectral representations for a class of banded Jacobi-type matrices [PDF]
Opuscula Mathematica, 2014 We describe some spectral representations for a class of non-self-adjoint banded Jacobi-type matrices. Our results extend those obtained by P.B. Naïman for (two-sided infinite) periodic tridiagonal Jacobi matrices.
Ewelina Zalot, Witold Majdak
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CAPACITIES AND JACOBI MATRICES [PDF]
Proceedings of the Edinburgh Mathematical Society, 2003 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 ...
Sebbar, Ahmed, Falliero, Thérèse
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Deficiency indices of block Jacobi matrices and Miura transformation
Special Matrices, 2022 We study the infinite Jacobi block matrices under the discrete Miura-type transformations which relate matrix Volterra and Toda lattice systems to each other and the situations when the deficiency indices of the corresponding operators are the same.
Osipov Andrey
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