Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle

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

Rakhmanov's theorem for orthogonal matrix polynomials on the unit circle

Rakhmanov’s theorem for orthogonal polynomials on the unit circle gives a sufficient condition on the orthogonality measure for orthogonal polynomials on the unit circle, in order that the reflection coefficients (the recurrence coefficients in the Szegő recurrence relation) converge to zero. In this paper we give the analog for orthogonal matrix polynomials on the unit circle. 1. Rakhmanov’s t...

متن کامل

Relative Asymptotics for Orthogonal Matrix Polynomials with Convergent Recurrence Coefficients

The asymptotic behavior of #n (d;) #n (d:) and Pn (x, d;) P n (x, d:) is studied. Here (#n (.))n are the leading coefficients of the orthonormal matrix polynomials Pn (x, .) with respect to the matrix measures d; and d: which are related by d;(u)= d:(u)+ k=1 Mk$(u&ck), where Mk are positive definite matrices, $ is the Dirac measure and ck lies outside the support of d: for k=1, ..., N. Finally,...

متن کامل

Elliptic polynomials orthogonal on the unit circle with respect to a singular continuous measure

We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a new type of elliptic hypergeometric function. We show that obtained polynomials are orthogonal on the unit circle with respect to a positive measure which is s...

متن کامل

Asymptotics of polynomials orthogonal over the unit disk with respect to a polynomial weight without zeros on the unit circle

We establish asymptotic formulas for polynomials that are orthogonal over the unit disk with respect to a weight of the form |w(z)|2, where w(z) is a polynomial without zeros on the unit circle |z| = 1. The formulas put in evidence a strong connection between the behavior of the polynomials and the reproducing kernel of an associated weighted Bergman space, which produces interesting new featur...

متن کامل

Asymptotics of derivatives of orthogonal polynomials on the unit circle

We show that ratio asymptotics of orthogonal polynomials on the circle imply ratio asymptotics for all their derivatives. Moreover, by reworking ideas of P. Nevai, we show that uniform asymptotics for orthogonal polynomials on an arc of the unit circle imply asymptotics for all their derivatives. Let be a …nite positive Borel measure on the unit circle (or [0; 2 ]). Let f'ng denote the orthonor...

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: Analysis in Theory and Applications

سال: 2002

ISSN: 1672-4070,1573-8175

DOI: 10.1007/bf02845271