Spectral Properties of Some Complex Jacobi Matrices
نویسندگان
چکیده
منابع مشابه
Spectral Properties of Some Combinatorial Matrices
In this paper we investigate the spectra and related questions for various combinatorial matrices, generalizing work by Carlitz, Cooper and Kennedy.
متن کاملComplex Jacobi Matrices
Complex Jacobi matrices play an important role in the study of asymptotics and zero distribution of Formal Orthogonal Polynomials (FOPs). The latter are essential tools in several elds of Numerical Analysis, for instance in the context of iterative methods for solving large systems of linear equations, or in the study of Pad e approximation and Jacobi continued fractions. In this paper we prese...
متن کاملOn a Spectral Property of Jacobi Matrices
Let J be a Jacobi matrix with elements bk on the main diagonal and elements ak on the auxiliary ones. We suppose that J is a compact perturbation of the free Jacobi matrix. In this case the essential spectrum of J coincides with [−2, 2], and its discrete spectrum is a union of two sequences {xj }, x + j > 2, x − j < −2, tending to ±2. We denote sequences {ak+1 − ak} and {ak+1 + ak−1 − 2ak} by ∂...
متن کاملSpectral averaging techniques for Jacobi matrices
Spectral averaging techniques for one-dimensional discrete Schrödinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under ...
متن کاملA spectral equivalence for Jacobi matrices
We use the classical results of Baxter and Gollinski-Ibragimov to prove a new spectral equivalence for Jacobi matrices on l(N). In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences, and find necessary and sufficient conditions on the spectral measure such that ∑ ∞ k=n bk and ∑ ∞ k=n (a k − 1) lie in l 1 ∩ l .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Integral Equations and Operator Theory
سال: 2020
ISSN: 0378-620X,1420-8989
DOI: 10.1007/s00020-020-2569-4