서지주요정보
Semi-classical and discrete orthogonal polynomials = 준고전 직교다항식과 이산 직교다항식
서명 / 저자 Semi-classical and discrete orthogonal polynomials = 준고전 직교다항식과 이산 직교다항식 / Suk-Bong Park.
발행사항 [대전 : 한국과학기술원, 1996].
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8006649

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DMA 96005

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First, we provide characterizations of semi-classical orthogonal polynomials via structure relations of any order≥1. Then we also obtain a new characterization of classical orthogonal polynomials, which generalizes Al-Salam and Chihara's characterization of classical orthogonal polynomials. We discuss the structure of distributional or hyperfunctional representation of semi-classical moment functionals. Next, we find a necessary and sufficient condition for the two point masses perturbation of a quasi-definite moment functional to have orthogonal polynomials and investigate zero properties of the corresponding orthogonal polynomials. Semi-classical characters of such orthogonal polynomials are also discussed. Secondly, we find the necessary and sufficient conditions for a second order difference equation of hypergeometric type: α(x)△▽y(x)+β(x)△y(x)=$λ_ny(x)$ to have discrete classical orthogonal polynomials as solutions. By the conditions, we show that the restrictions on parameters for each discrete classical orthogonal polynomials can be relaxed when we consider orthogonal polynomials relative to quasi-definite moment functionals and also derive functional Rodrigues' formula for discrete classical orthogonal polynomials. Finally, we discuss various characterizations of Hahn type orthogonal polynomials, which are first introduced by Hahn in 1949. He introduced a operator, now called Hahn operator: δf(x):=$\frac{f(qx+ω)-f(x)}{(q-1)x+ω}$ which include the differential and finite difference operators as limiting cases, and operator equations which are satisfied by orthogonal polynomials. Here, we introduce new operator equations which are equivalent to Hahn operator equations and then obtain unified characterizations extending all results of classical and discrete classical orthogonal polynomials.

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서지기타정보
청구기호 {DMA 96005
형태사항 [iii], 71 p. : 삽도 ; 25 cm
언어 영어
일반주기 저자명의 한글표기 : 박석봉
지도교수의 영문표기 : Kil-Hyun Kwon
지도교수의 한글표기 : 권길헌
학위논문 학위논문(박사) - 한국과학기술원 : 수학과,
서지주기 Reference : p. 69-71
주제 Semi-classical orthogonal polynomial
quasi-definite moment functional
Discrete orthogonal polynomial
Hahn type orthogonal polynomial
준고전 직교다항식
의사 정치 범함수
이산 직교다항식
Hahn 형태 직교다항식
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