Hyperfunctional Weights for Orthogonal Polynomials

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The Chebychev polynomials associated to any given moments μn ∞ 0 are formally orthogonal with respect to the formal δ-series w(x)=∑ 0 ∞ (−1) n μ n δ (n) (x)/n!. We show that this formal weight can be a true hyperfunctional weight if its Fourier transform is a slowly increasing holomorphic function in some tubular neighborhood of the real line. It provides a unifying treatment of real and complex orthogonality of Chebychev polynomials including all classical examples and characterizes Chebychev polynomials having Bessel type orthogonality.
Publisher
Birkhauser Verlag Ag
Issue Date
1990-11
Language
English
Citation

RESULTS IN MATHEMATICS, v.18, no.3-4, pp.273 - 281

ISSN
1422-6383
URI
http://hdl.handle.net/10203/64261
Appears in Collection
MA-Journal Papers(저널논문)
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