Green Matrix Estimates of Block Jacobi Matrices II: Bounded Gap in the Essential Spectrum

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Elementary Models of Unbounded Jacobi Matrices with a Few Bounded Gaps in the Essential Spectrum

This work contains a constructive example of a class of Jacobi operators with an arbitrary finite number of gaps in its unbounded essential spectrum. The construction of this class is based on elementary ideas of gluing finite-dimensional Jacobi matrices whose sizes grow to infinity. The precise analysis of the finite-dimensional pieces leads to a new “finite essential spectrum” besides the nat...

متن کامل

Spectral gap estimates for some block matrices

We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices which need not belong to either of these classes. Matrices of such structure arise in quantum models of possibly disordered systems with supersymmetry or graph...

متن کامل

Finite Gap Jacobi Matrices, Ii. the Szegő Class

Let e ⊂ R be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szegő condition is equivalent to lim sup a1 · · · an cap(e) > 0 (this includes prior results of Widom and Peherstorfer–Yuditskii). Using Remling’s extension of the Denisov–Rakhmanov theorem and an analysis of Jost func...

متن کامل

The absolutely continuous spectrum of Jacobi matrices

I explore some consequences of a groundbreaking result of Breimesser and Pearson on the absolutely continuous spectrum of one-dimensional Schrödinger operators. These include an Oracle Theorem that predicts the potential and rather general results on the approach to certain limit potentials. In particular, we prove a Denisov-Rakhmanov type theorem for the general finite gap case. The main theme...

متن کامل

Green ’ s matrix from Jacobi - matrix Hamiltonian ∗

We propose two ways for determining the Green’s matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from the Jacobi-matrix, the first approach also requires the matrix elements of the Green’s operator between the first elements of the basis. In the second approa...

متن کامل

ذخیره 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/s00020-020-02576-7