Asymptotics of Sobolev Orthogonal Polynomials for Coherent Pairs of Laguerre Type
نویسندگان
چکیده
Let Snn denote a sequence of polynomials orthogonal with respect to the Sobolev inner product f; gS = ∫ f xgxdψ0x + λ ∫ f xgxdψ1x; where λ > 0 and dψ0; dψ1 is a so-called coherent pair with at least one of the measures dψ0 or dψ1 a Laguerre measure. We investigate the asymptotic behaviour of Snx outside the supports of dψ0 and dψ1, and n→+∞. © 2000 Academic Press
منابع مشابه
Laguerre-Sobolev orthogonal polynomials: asymptotics for coherent pairs of type II
Let Sn be polynomials orthogonal with respect to the inner product ð f ; gÞS 1⁄4 Z N
متن کاملAsymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures
Inner products of the type 〈f, g〉S = 〈f, g〉ψ0 + 〈f ′, g〉ψ1, where one of the measures ψ0 or ψ1 is the measure associated with the Jacobi polynomials, are usually referred to as Jacobi-Sobolev inner products. This paper deals with some asymptotic relations for the orthogonal polynomials with respect to a class of Jacobi-Sobolev inner products. The inner products are such that the associated pair...
متن کاملMonotonicity and Asymptotics of Zeros of Laguerre-sobolev-type Orthogonal Polynomials of Higher Order Derivatives
In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product
متن کاملStrong and Plancherel-Rotach Asymptotics of Non-diagonal Laguerre-Sobolev Orthogonal Polynomials
when :>0. In this way, the measure which appears in the first integral is not positive on [0, ) for + # R" [&1, 0]. The aim of this paper is the study of analytic properties of the polynomials Qn . First we give an explicit representation for Qn using an algebraic relation between Sobolev and Laguerre polynomials together with a recursive relation for k n=(Qn , Qn)S . Then we consider analytic ...
متن کاملA new approach to the asymptotics of Sobolev type orthogonal polynomials
This paper deals with Mehler-Heine type asymptotic formulas for so called discrete Sobolev orthogonal polynomials whose continuous part is given by Laguerre and generalized Hermite measures. We use a new approach which allows to solve the problem when the discrete part contains an arbitrary (finite) number of mass points. 2000MSC: 42C05, 33C45.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997