서지주요정보
Study of ordinary differential equations in the space of hyperfunctions and its applications to orthogonal polynomials = 초함수공간에서의 상미분방정식의 연구와 직교다항식에의 응용
서명 / 저자 Study of ordinary differential equations in the space of hyperfunctions and its applications to orthogonal polynomials = 초함수공간에서의 상미분방정식의 연구와 직교다항식에의 응용 / Sung-Soo Kim.
발행사항 [대전 : 한국과학기술원, 1991].
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8002274

소장위치/청구기호

학술문화관(문화관) 보존서고

DAM 9103

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As a kind of generalized functions, hyperfunctions are, in some sense, more naturally adapted to the study of partial differential equations than L. Schwartz's distributions. For example, the microlocal analysis of differential operators, which is now an indispensable tool in the development of the theory of differential equations, comes very naturally from the hyperfunctional viewpoint. We first extend the celebrated theorem bt H. Komatsu on the index of ordinary differential operators with analytic coefficients on the space of hyperfunctions to the index theorem of the microdifferential operators on the space of microfunctions. In particular, we prove the surjectivity of the microdifferential operators on the space of microfunctions. The latter together with the index theorem gives an elegant formula for the number of linearly independent solutions of homogeneous microdifferential equations. Secondly, we apply the theory of hyperfunctions to the study of orthogonal polynomials. Use of hyperfunction theory in the study of orthogonal polynomials not only answers many fundamental questions arising in the field of orthogonal polynomials but also opens a new way of investigating them. In particular, via the Fourier hyperfunction, we unify the real and complex orthogonality of Tchebychev ploynomial sets under a single theory, and find a net complex orthogonality of Laguerre polynomials, and answer to the open question, raised by E. Grosswald, of characterizing orthogonal polynomials having the Bessel type orthogonality. Finally, we construct a bounded variation measure in a closed form with respect to which Bessel polynomials are orthogonal. It resolves the long standing open problem of finding a real orthogonalizing weight of bounded variation for Bessel polynomials, which was first raised by, H. L. Krall and O.Frink and remained enigmatic for the last forty years.

서지기타정보

서지기타정보
청구기호 {DAM 9103
형태사항 [ii], 57 p. : 삽화 ; 26 cm
언어 영어
일반주기 저자명의 한글표기 : 김성수
지도교수의 영문표기 : Kil-Hyun Kwon
지도교수의 한글표기 : 권길헌
학위논문 학위논문(박사) - 한국과학기술원 : 수학과,
서지주기 Reference : p. 54-57
주제 Hyperfunctions
Orthogonal polynomials
상미분 방정식 --과학기술용어시소러스
초함수 --과학기술용어시소러스
직교 함수 --과학기술용어시소러스
Differential equations
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