Recurrence and asymptotics for orthonormal rational functions on an interval
نویسندگان
چکیده
منابع مشابه
Ratio asymptotics for orthogonal rational functions on an interval
Let {α1, α2, . . . } be a sequence of real numbers outside the interval [−1, 1] and μ a positive bounded Borel measure on this interval satisfying the Erdős-Turán condition μ′ > 0 a.e., where μ′ is the RadonNikodym derivative of the measure μ with respect to the Lebesgue measure. We introduce rational functions φn(x) with poles {α1, . . . , αn} orthogonal on [−1, 1] and establish some ratio asy...
متن کاملRational Orthonormal Functions and Applications
Acknowledgement I am very grateful to Professor Ferenc Schipp for initiating me on the field of the approximation theory, for his advices and remarks without them this thesis would have been impossible. I am also indebted to the members of the Department of Numerical Analysis of the Eötvös Loránd University for their support during the years. I am especially grateful to Professor József Bokor i...
متن کاملRatio Asymptotics for Orthogonal Rational Functions on the Interval [−1, 1]
Let {α1, α2, . . . } be a sequence of real numbers outside the interval [−1, 1] and μ a positive bounded Borel measure on this interval. We introduce rational functions φn(x) with poles {α1, . . . , αn} orthogonal on [−1, 1] and establish some ratio asymptotics for these orthogonal rational functions, i.e. we discuss the convergence of φn+1(x)/φn(x) as n tends to infinity under certain assumpti...
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We use Freud equations to obtain the main term in the asymptotic expansion of the recurrence coefficients associated with orthonormal polynomials pn(w) for weights w = W exp(−Q) on the real line where Q is an even polynomial of fixed degree with nonnegative coefficients or where Q(x) = exp(x2m), m ≥ 1. Here W (x) = |x|ρ for some real ρ > −1.
متن کاملRecurrence relations for orthogonal rational functions
It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arb...
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ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2008
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drm048