Hyperfunctional Weights for Orthogonal Polynomials |
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Authors: | Sung S Kim Kil H Kwon |
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Institution: | 1. Department of Applied Mathematics, KAIST, P.O.Box 150, Cheongryang, Seoul, 130-650, Korea
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Abstract: | The Chebychev polynomials associated to any given moments μn ∞ 0 are formally orthogonal with respect to the formal δ-series $$w(x)= {\sum^\infty_0}(- 1)^{n}\mu_{{n}}\delta^{(n)}(x)/n!.$$ 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. |
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