Spectral Properties of Block Jacobi Matrices
نویسندگان
چکیده
منابع مشابه
Equivalence Classes of Block Jacobi Matrices
The paper contains two results on the equivalence classes of block Jacobi matrices: first, that the Jacobi matrix of type 2 in the Nevai class has An coefficients converging to 1, and second, that under an L1-type condition on the Jacobi coefficients, equivalent Jacobi matrices of types 1, 2 and 3 are pairwise asymptotic.
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 properties of unbounded JJ-self-adjoint block operator matrices
We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient condition for the spectrum being real and derive variational principles for certain real eigenvalues even in the presence of non-real spectrum. The latter lead to lower and upper bounds and asymptotic estimates for eigenvalues. AMS Subject classifi...
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: Constructive Approximation
سال: 2018
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-018-9420-z