Finite Gap Jacobi Matrices and the Schottky–Klein Prime Function
نویسندگان
چکیده
منابع مشابه
Finite gap Jacobi matrices: An announcement
We consider Jacobi matrices whose essential spectrum is a finite union of closed intervals. We focus on Szegő’s theorem, Jost solutions, and Szegő asymptotics for this situation. This announcement describes talks the authors gave at OPSFA 2007.
متن کاملFinite Gap Jacobi Matrices: A Review
Perhaps the most common theme in Fritz Gesztesy’s broad opus is the study of problems with periodic or almost periodic finite gap differential and difference equations, especially those connected to integrable systems. The present paper reviews recent progress in the understanding of finite gap Jacobi matrices and their perturbations. We’d like to acknowledge our debt to Fritz as a collaborator...
متن کاملFinite 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 کاملFinite Gap Jacobi Matrices, III. Beyond the Szegő Class
Let e ⊂ R be a finite union of + 1 disjoint closed intervals, and denote by ωj the harmonic measure of the j left-most bands. The frequency module for e is the set of all integral combinations of ω1, . . . ,ω . Let {ãn, b̃n}∞n=−∞ be a point in the isospectral torus for e and p̃n its orthogonal polynomials. Let {an, bn}∞n=1 be a half-line Jacobi matrix with an = ãn + δan, bn = b̃n + δbn. Suppose ∞ ...
متن کاملFinite Gap Jacobi Matrices, I. The Isospectral Torus
Let e⊂ R be a finite union of disjoint closed intervals. In the study of orthogonal polynomials on the real line with measures whose essential support is e, a fundamental role is played by the isospectral torus. In this paper, we use a covering map formalism to define and study this isospectral torus. Our goal is to make a coherent presentation of properties and bounds for this special class as...
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: Computational Methods and Function Theory
سال: 2016
ISSN: 1617-9447,2195-3724
DOI: 10.1007/s40315-016-0186-7