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Volume 27 Number 3 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/475

Title: Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order
Authors: Zagorodniuk, S.
Keywords: Orthogonal Polynomials
Difference Equation
Issue Date: 2001
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 27, No 3, (2001), 193p-202p
Abstract: Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, . . ., α−1 = α−2 = β−1 = 0, p−1 = p−2 = 0, p0 (λ) = 1, p1 (λ) = cλ + b, c > 0, b ∈ C, λ ∈ C. It is shown that they are orthonormal on the real and the imaginary axes in the complex plane ...
URI: http://hdl.handle.net/10525/475
ISSN: 1310-6600
Appears in Collections:Volume 27 Number 3

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