Zero distribution of orthogonal polynomials직교다항식의 근의 분포

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In [5], Karlin and Szego conjectured : If ${P_n(x)}^∞_{n=0}$ is an orthogonal polynomial system and ${P``_{n}(x)}^∞_{n=1}$ is a Sturm sequence, then ${P_n(x)}^∞_{n=0}$ is essentially (that is, after a linear change of variable) a classical orthogonal polynomial system of Jacobi, Laguerre, or Hermite. Here, we prove that for any orthogonal polynomial system ${P_n(x)}^∞_{n=0}$, ${P``_{n}(x)}^∞_{n=1}$ is always a Sturm sequence. Thus, in particular, the above conjecture by Karlin and Szeg$ö$ is false. And zero distribution of the polynomials ${S_{n}(x)}^∞_{n=0}$ which are orthogonal with respect to the discrete Sobolev inner product type. <f,g> = ∫_If(x)g(x)dμ(x)+$Nf^{(r)}(c)g^{(r)}(c)$ where I is a real interval, with I = [a,b], a,b ∈ R, N ≥ 0, r ≥ 1, c ≥ b and let μ(x) be an arbitrary distribution function on I. $S_{n}(x)$ has n real, simple zeros. The location of these zeros is given in relation to the position of the zeros of some classical polynomials (i.e., polynomials with respect to an inner product with N=0).
Advisors
Kwon, Kil-Hunresearcher권길헌researcher
Description
한국과학기술원 : 수학과,
Publisher
한국과학기술원
Issue Date
1995
Identifier
98711/325007 / 000933045
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수학과, 1995.2, [ [ii], 20 p. ]

URI
http://hdl.handle.net/10203/42398
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=98711&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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