Recurrence Coefficients of Orthogonal Polynomials with Respect to Some Self-Similar Singular Distributions
نویسندگان
چکیده
منابع مشابه
Orthogonal Polynomials with Respect to Self-Similar Measures
We study experimentally systems of orthogonal polynomials with respect to self-similar measures. When the support of the measure is a Cantor set, we observe some interesting properties of the polynomials, both on the Cantor set and in the gaps of the Cantor set. We introduce an effective method to visualize the graph of a function on a Cantor set. We suggest a new perspective, based on the theo...
متن کاملVarying weights for orthogonal polynomials with monotonically varying recurrence coefficients
and the coefficients in (1.3), which depend on the parameter N , {an,N : bn,N}n=0, bn,N > 0. ∗The authors acknowledge support from NATO Collaborative linkage grant PST.CLG.979738 and INTAS Research Network 03-51-6637. The first author was supported by grants RFBR-05-01-00522, NSh1551.2003.1, Program No. 1 DMS RAS. The second author was supported by an NSF grant. The third author was supported b...
متن کاملRatio Asymptotics for Orthogonal Matrix Polynomials with Unbounded Recurrence Coefficients
In this work is presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients. The ratio asymptotic for this family of matrix biorthogonal polynomials is derived in quite general assumptions. It is considered some illustrative examples.
متن کاملRelative 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 کاملDiscrete Painlevé equations for recurrence coefficients of orthogonal polynomials
The converse statement is also true and is known as the spectral theorem for orthogonal polynomials : if a family of polynomials satisfies a three-term recurrence relation of the form (1.2), with an > 0 and bn ∈ R and initial conditions p0 = 1 and p−1 = 0, then there exists a probability measure μ on the real line such that these polynomials are orthonormal polynomials satisfying (1.1). This gi...
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: Zeitschrift für Analysis und ihre Anwendungen
سال: 1995
ISSN: 0232-2064
DOI: 10.4171/zaa/667