On the linear functionals associated to linearly related sequences of orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Orthogonal polynomials for refinable linear functionals
A refinable linear functional is one that can be expressed as a convex combination and defined by a finite number of mask coefficients of certain stretched and shifted replicas of itself. The notion generalizes an integral weighted by a refinable function. The key to calculating a Gaussian quadrature formula for such a functional is to find the three-term recursion coefficients for the polynomi...
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We consider the non-de nite linear functionals Ln[f] = ∫ R w(x)f (x) dx and prove the nonexistence of orthogonal polynomials, with all zeros real, in several cases. The proofs are based on the connection with moment preserving spline approximation. c © 1998 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.05.018