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1.
Timothy Nguyen 《Journal of Mathematical Analysis and Applications》2007,327(2):977-990
Consider ergodic orthogonal polynomials on the unit circle whose Verblunsky coefficients are given by αn(ω)=λV(Tnω), where T is an expanding map of the circle and V is a C1 function. Following the formalism of [Jean Bourgain, Wilhelm Schlag, Anderson localization for Schrödinger operators on Z with strongly mixing potentials, Comm. Math. Phys. 215 (2000) 143-175; Victor Chulaevsky, Thomas Spencer, Positive Lyapunov exponents for a class of deterministic potentials, Comm. Math. Phys. 168 (1995) 455-466], we show that the Lyapunov exponent γ(z) obeys a nice asymptotic expression for λ>0 small and z∈∂D?{±1}. In particular, this yields sufficient conditions for the Lyapunov exponent to be positive. Moreover, we also prove large deviation estimates and Hölder continuity for the Lyapunov exponent. 相似文献
2.
3.
A. Branquinho A. Foulqui Moreno F. Marcelln M.N. Rebocho 《Journal of Approximation Theory》2008,153(1):122-137
In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if (μ0,μ1) is a coherent pair of measures on the unit circle, then μ0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with μ1 is a specific rational transformation of the linear functional corresponding to μ0. Some examples are given. 相似文献
4.
C. Suárez 《Journal of Mathematical Analysis and Applications》2009,358(1):148-158
In this paper the following construction process of orthogonal polynomials on the unit circle is considered: Let u be a regular and hermitian linear functional and let {Φn} be the corresponding orthogonal polynomials sequence. We define a new linear functional L by means the following relation with u:
5.
A scalar Riemann boundary value problem defining orthogonal polynomials on the unit circle and the corresponding functions of the second kind is obtained. The Riemann problem is used for the asymptotic analysis of the polynomials orthogonal with respect to an analytical real-valued weight on the circle. 相似文献
6.
Francisco Marcellán Franz Peherstorfer Robert Steinbauer 《Advances in Computational Mathematics》1996,5(1):281-295
Let {P
n
} be a sequence of orthogonal polynomials with respect to the measured on the unit circle and letP
n
=P
n
+
j
=1l
nj
P
n–j
fornl, where
n,j
. It is shown that the sequence of linear combinations {P
n
},n2l, is orthogonal with respect to a positive measured if and only ifd is a Bernstein-Szegö measure andd is the product of a unique trigonometric polynomial and the Bernstein-Szegö measured. Furthermore for a given sequence ofP
n
's an algorithm for the calculation of the
n,j
's is provided.Supported by Dirección General de Investigación Cientifica y Técnica (DGICYT) of Spain and Österreichischer Akademischer Austauschdienst of Austria with grant 4B/1995.Also supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, project-number P9267-PHY. 相似文献
7.
For a sequence of monic orthogonal polynomials (SMOP), with respect to a positive measure supported on the unit circle, we obtain necessary and sufficient conditions on a SMOP in order that a convex linear combination with be a SMOP with respect to a positive measure supported on the unit circle.
8.
This paper deals with modifications of the Lebesgue moment functional by trigonometric polynomials of degree 2 and their associated orthogonal polynomials on the unit circle. We use techniques of five-diagonal matrix factorization and matrix polynomials to study the existence of such orthogonal polynomials.Dedicated to Prof. Luigi Gatteschi on his 70th birthdayThis research was partially supported by Diputación General de Aragón under grant P CB-12/91. 相似文献
9.
Yuan Xu 《Proceedings of the American Mathematical Society》2005,133(7):1965-1976
For a class of weight functions invariant under reflection groups on the unit ball, a family of orthogonal polynomials is defined via a Rodrigues type formula using the Dunkl operators. Their properties and their relation with several other bases are explored.
10.
Some examples of orthogonal matrix polynomials satisfying odd order differential equations 总被引:1,自引:1,他引:1
It is well known that if a finite order linear differential operator with polynomial coefficients has as eigenfunctions a sequence of orthogonal polynomials with respect to a positive measure (with support in the real line), then its order has to be even. This property no longer holds in the case of orthogonal matrix polynomials. The aim of this paper is to present examples of weight matrices such that the corresponding sequences of matrix orthogonal polynomials are eigenfunctions of certain linear differential operators of odd order. The weight matrices are of the form
W(t)=tαe-teAttBtB*eA*t,