DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kwon, Kil-Hun | - |
dc.contributor.advisor | 권길헌 | - |
dc.contributor.author | Kim, Deok-Ho | - |
dc.contributor.author | 김덕호 | - |
dc.date.accessioned | 2011-12-14T04:59:37Z | - |
dc.date.available | 2011-12-14T04:59:37Z | - |
dc.date.issued | 1995 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=98711&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/42398 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수학과, 1995.2, [ [ii], 20 p. ] | - |
dc.description.abstract | 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). | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.title | Zero distribution of orthogonal polynomials | - |
dc.title.alternative | 직교다항식의 근의 분포 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 98711/325007 | - |
dc.description.department | 한국과학기술원 : 수학과, | - |
dc.identifier.uid | 000933045 | - |
dc.contributor.localauthor | Kwon, Kil-Hun | - |
dc.contributor.localauthor | 권길헌 | - |
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