Universality under Szegő ’ s condition ∗
نویسنده
چکیده
This paper presents a theorem on universality on orthogonal polynomials/random matrices under a weak local condition on the weight function w. With a new inequality for polynomials and with the use of fast decreasing polynomials, it is shown that an approach of D. S. Lubinsky is applicable. The proof works at all points which are Lebesgue-points both for the weight function w and for logw.
منابع مشابه
Anti-Szego quadrature rules
Szegő quadrature rules are discretization methods for approximating integrals of the form ∫ π −π f(e it)dμ(t). This paper presents a new class of discretization methods, which we refer to as anti-Szegő quadrature rules. AntiSzegő rules can be used to estimate the error in Szegő quadrature rules: under suitable conditions, pairs of associated Szegő and anti-Szegő quadrature rules provide upper a...
متن کاملJost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics
We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence of Szegő asymptotics and of Jost asymptotics for the Weyl solution. We also prove L2 convergence of Szegő asymptotics on the spectrum.
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 کاملInvariantly Universal Analytic Quasi - Orders Riccardo
We introduce the notion of an invariantly universal pair (S, E) where S is an analytic quasi-order and E ⊆ S ∩S is an analytic equivalence relation. This means that for any analytic quasi-order R there is a Borel set B invariant under E such that R is Borel equivalent to the restriction of S to B. We prove a general result giving a sufficient condition for invariant universality, and we demonst...
متن کاملNew Bounds for the Principal Dirichlet Eigenvalue of Planar Regions
where j0,1 is the first positive zero of the Bessel function J0, and equality holds for the disk. If we now restrict the class of domains under consideration, it is possible to improve the above result. This can be done in several different ways, of which we shall now discuss some examples. One possibility is to consider the class of n-polygons, for which Pólya and Szegő proposed the following ...
متن کامل