Results 1 to 10 of about 36 (36)

Inverse spectral problem for Jacobi operators and Miura transformation

Concrete Operators, 2021
We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems.
Osipov Andrey
doaj   +1 more source

Schrödinger’s tridiagonal matrix

Special Matrices, 2021
In the third part of his famous 1926 paper ‘Quantisierung als Eigenwertproblem’, Schrödinger came across a certain parametrized family of tridiagonal matrices whose eigenvalues he conjectured.
Kovačec Alexander
doaj   +1 more source

On some reciprocal matrices with elliptical components of their Kippenhahn curves

Special Matrices, 2021
By definition, reciprocal matrices are tridiagonal n-by-n matrices A with constant main diagonal and such that ai,i+1ai+1,i= 1 for i = 1, . . ., n − 1.
Jiang Muyan, Spitkovsky Ilya M.
doaj   +1 more source

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
doaj   +1 more source

Explicit solution for an infinite dimensional generalized inverse eigenvalue problem

International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 9, Page 513-523, 2001., 2001
We study a generalized inverse eigenvalue problem (GIEP), Ax = λBx, in which A is a semi‐infinite Jacobi matrix with positive off‐diagonal entries ci > 0, and B = diag (b0, b1, …), where bi ≠ 0 for i = 0, 1, …. We give an explicit solution by establishing an appropriate spectral function with respect to a given set of spectral data.
Kazem Ghanbari
wiley   +1 more source

A class of tridiagonal operators associated to some subshifts

Open Mathematics, 2016
We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ...
Hernández-Becerra Christian, Itzá-Ortiz Benjamín A.   +1 more
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Cantor spectrum for multidimensional quasi-periodic Schrödinger operators

Forum of Mathematics, Sigma
In this paper, we prove that for a dense set of irrational frequencies with positive Hausdorff dimension, the Hausdorff (and upper box) dimension of the spectrum of the critical almost Mathieu operator is positive, yet can be made arbitrarily small. As a
Bernard Helffer, Qinghui Liu, Yanhui Qu, Qi Zhou   +3 more
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Nonperturbative localization on the strip and Avila’s almost reducibility conjecture

Forum of Mathematics, Pi
We prove nonperturbative Anderson localization and almost localization for a family of quasi-periodic operators on the strip. As an application, we establish Avila’s almost reducibility conjecture for Schrödinger operators with trigonometric potentials ...
Rui Han, Wilhelm Schlag
doaj   +1 more source

Block diagonalization of (p, q)-tridiagonal matrices

Special Matrices
In this article, we study the block diagonalization of (p,q)\left(p,q)-tridiagonal matrices and derive closed-form expressions for the number and structure of diagonal blocks as functions of the parameters pp, qq, and nn. This reduction enables efficient
Manjunath Hariprasad
doaj   +1 more source

Inhomogeneous isotropic quantum spin chain associated with the difference Lamé equation

Forum of Mathematics, Sigma
The spectrum and orthogonal eigenbasis are computed of a tridiagonal matrix encoding a finite-dimensional reduction of the difference Lamé equation at the single-gap integral value of the coupling parameter.
Jan Felipe van Diejen
doaj   +1 more source