Results 21 to 30 of about 511,937 (269)
The Szegő condition for Coulomb Jacobi matrices
Journal of Approximation Theory, 2003 A Jacobi matrix with $a_n\to 1$, $b_n\to 0$ and spectral measure $ '(x)dx + d _{sing}(x)$ satisfies the Szeg\H o condition if $\int_{0}^ \ln \bigl[ '(2\cos ) \bigr] d $ is finite. We prove that if $a_n = 1 + \frac {n} + O(n^{-1-\eps})$ and $b_n = \frac {n} + O(n^{-1-\eps})$ with $2 \ge | |$ and $\eps>0$, then the corresponding matrix is
Andrej Zlatoš
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Jacobi matrices with lacunary spectrum [PDF]
Journal of Mathematical Analysis and Applications, 2020 We find asymptotics of entries of Jacobi matrices with lacunary spectral data under some additional growth conditions. We also prove the inverse results. In addition, we study connections between Jacobi matrices, canonical systems and de Branges spaces for lacunary spectral ...
I. Losev
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A Note on Reflectionless Jacobi Matrices [PDF]
Communications in Mathematical Physics, 2014 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 terms of stationary scattering theory (the vanishing of the reflection coefficients) and prove that
Jaksic, Vojkan +2 more
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Spectral resolutions for non-self-adjoint block convolution operators [PDF]
Opuscula Mathematica, 2022 The paper concerns the spectral theory for a class of non-self-adjoint block convolution operators. We mainly discuss the spectral representations of such operators. It is considered the general case of operators defined on Banach spaces.
Ewelina Zalot
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Asymptotics of the discrete spectrum for complex Jacobi matrices [PDF]
Opuscula Mathematica, 2014 The spectral properties and the asymptotic behaviour of the discrete spectrum for a special class of infinite tridiagonal matrices are given. We derive the asymptotic formulae for eigenvalues of unbounded complex Jacobi matrices acting in \(l^2(\mathbb{N}
Maria Malejki
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Titchmarsh–Weyl Formula for the Spectral Density of a Class of Jacobi Matrices in the Critical Case [PDF]
Functional analysis and its applications, 2019 We consider a class of Jacobi matrices with unbounded entries in the so-called critical (double root, Jordan block) case. We prove a formula which relates the spectral density of a matrix to the asymptotics of orthogonal polynomials associated with it.
S. Naboko, S. Simonov
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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 ...
Thérèse Falliero, Ahmed Sebbar
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Perturbation series for Jacobi matrices and the quantum Rabi model [PDF]
Opuscula Mathematica, 2021 We investigate eigenvalue perturbations for a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum.
Mirna Charif, Lech Zielinski
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An operational approach for solving fractional pantograph differential equation [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2019 The aim of the current paper is to construct the shifted fractional-order Jacobi functions (SFJFs) based on the Jacobi polynomials to numerically solve the fractional-order pantograph differential equations. To achieve this purpose, first the operational
H. Ebrahimi, K. Sadri
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Spectral Properties of Some Complex Jacobi Matrices [PDF]
Integral equations and operator theory, 2019 We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide uniform ...
Grzegorz Świderski
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