Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures
نویسندگان
چکیده
منابع مشابه
Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures
Let be a finite positive Borel measure with compact support consisting of an interval [c, d] ⊂ R plus a set of isolated points in R\[c, d], such that ′> 0 almost everywhere on [c, d]. Let {w2n}, n ∈ Z+, be a sequence of polynomials, degw2n 2n, with real coefficients whose zeros lie outside the smallest interval containing the support of . We prove ratio and relative asymptotics of sequences of ...
متن کاملRelative Asymptotics of Orthogonal Polynomials for Perturbed Measures
We survey and present some new results that are related to the behavior of orthogonal polynomials in the plane under small perturbations of the measure of orthogonality. More precisely, we introduce the notion of a polynomially small (PS) perturbation of a measure. Namely, if μ0 ≥ μ1 and {pn(μj , z)}n=0, j = 0, 1, are the associated orthonormal polynomial sequences, then μ0 a PS perturbation of...
متن کاملAsymptotics of Laurent Polynomials of Even Degree Orthogonal with Respect to Varying Exponential Weights
Let Λ denote the linear space over R spanned by z, k ∈Z. Define the real inner product (with varying exponential weights) 〈·, ·〉L : Λ ×ΛR→R, ( f , g) 7→ ∫ R f (s)g(s) exp(−N V(s)) ds, N∈N, where the external fieldV satisfies: (i)V is real analytic onR\ {0}; (ii) lim|x|→∞(V(x)/ ln(x2+1))=+∞; and (iii) lim|x|→0(V(x)/ ln(x−2+1))=+∞. Orthogonalisation of the (ordered) base {1, z−1, z, z−2, z2, . . ...
متن کاملAsymptotics of Laurent Polynomials of Odd Degree Orthogonal with Respect to Varying Exponential Weights
Let Λ denote the linear space over R spanned by z, k ∈Z. Define the real inner product (with varying exponential weights) 〈·, ·〉L : Λ ×ΛR→R, ( f , g) 7→ ∫ R f (s)g(s) exp(−N V(s)) ds, N∈N, where the external fieldV satisfies: (i)V is real analytic onR\ {0}; (ii) lim|x|→∞(V(x)/ ln(x2+1))=+∞; and (iii) lim|x|→0(V(x)/ ln(x−2+1))=+∞. Orthogonalisation of the (ordered) base {1, z−1, z, z−2, z2, . . ...
متن کاملRelative Asymptotics for Polynomials Orthogonal with Respect to a Discrete Sobolev Inner Product
We investigate the asymptotic properties of orthogonal polynomials for a class of inner products including the discrete Sobolev inner products 〈h, g〉 = ∫ hg dμ+ ∑m j=1 Nj i=0 Mj,ih (cj)g (cj), where μ is a certain type of complex measure on the real line, and cj are complex numbers in the complement of supp(μ). The Sobolev orthogonal polynomials are compared with the orthogonal polynomials corr...
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: Journal of Approximation Theory
سال: 2006
ISSN: 0021-9045
DOI: 10.1016/j.jat.2005.08.006