Discrete Orthogonal Polynomial Expansions of Averaged Functions
β Scribed by I. Fischer
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 328 KB
- Volume
- 194
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
We prove that if both [P n (x)] n=0 and [{ r P n (x)] n=r are orthogonal polynomials for any fixed integer r 1, then [P n (x)] n=0 must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahn's theorem stating that if both [P n (x)] n=0 and [(dΓdx) r P n
## Abstract Let __d__ΞΌ(__x__) = (1 β __x__^2^)^Ξ±β1/2^__dx__,Ξ±> β 1/2, be the Gegenbauer measure on the interval [ β 1, 1] and introduce the nonβdiscrete Sobolev inner product where Ξ»>0. In this paper we will prove a Cohen type inequality for Fourier expansions in terms of the polynomials orthogona