Results 41 to 50 of about 511,937 (269)
Block Jacobi matrices and Titchmarsh-Weyl function [PDF]
Opuscula MathematicaWe collect some results and notions concerning generalizations for block Jacobi matrices of several concepts, which have been important for spectral studies of the simpler and better known scalar Jacobi case.
Marcin Moszyński, Grzegorz Świderski
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On Commutators and Jacobi Matrices [PDF]
Proceedings of the American Mathematical Society, 1956 The closure, W, of the set of values (Cx, x) when ||x|| = 1 is a closed convex set (Hausdorff, cf. [8, p. 34]). A complex number z will be said to belong to the interior of W if z is in W and if one of the following conditions holds: (i) If W is two-dimensional, then z does not lie on the boundary of W; (ii) If W is a line segment, then z is not an end
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Inhomogeneous Jacobi Matrices on Trees [PDF]
Constructive Approximation, 2018 We study Jacobi matrices on trees with one end at inifinity. We show that the defect indices cannot be greater than 1 and give criteria for essential selfadjointness. We construct certain polynomials associated with matrices, which mimic orthogonal polynomials in the classical case. Nonnegativity of Jacobi matrices is studied as well.
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A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry
Advances in Mathematical Physics, 2018 The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the 2M-dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new polynomial identity ...
S. B. Rutkevich
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Localization of Discrete Time Quantum Walks on the Glued Trees
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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Homology of Lie algebras of orthogonal and symplectic generalized Jacobi matrices [PDF]
, 2018 In this note, we compute the homology with trivial coefficients of Lie algebras of generalized Jacobi matrices of type $B, C$ and $D$ over an associative unital $k$-algebra with $k$ being a field of characteristic $0$.
A. Fialowski, K. Iohara
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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? For example, can we approximate by periodic operators?
Christian Remling, Alexei Poltoratski
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Batched Eigenvalue Decomposition Algorithms for Hermitian Matrices on GPU [PDF]
Jisuanji kexue, 2023 Batched matrix computing problems are widely existed in scientific computing and engineering applications.With rapid performance improvements,GPU has become an important tool to solve such problems.The eigenvalue decomposition belongs to the two-sided ...
HUANG Rongfeng, LIU Shifang, ZHAO Yonghua
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CMV: The unitary analogue of Jacobi matrices [PDF]
Communications on Pure and Applied Mathematics, 2006 AbstractWe discuss a number of properties of CMV matrices, by which we mean the class of unitary matrices studied recently by Cantero, Moral, and Velázquez. We argue that they play an equivalent role among unitary matrices to that of Jacobi matrices among all Hermitian matrices.
Irina Nenciu, Irina Nenciu, Rowan Killip
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Ergodic Jacobi Matrices and Conformal Maps [PDF]
Mathematical Physics, Analysis and Geometry, 2012 We study structural properties of the Lyapunov exponent $ $ and the density of states $k$ for ergodic (or just invariant) Jacobi matrices in a general framework. In this analysis, a central role is played by the function $w=- +i k$ as a conformal map between certain domains.
Injo Hur, Christian Remling
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