Zero distribution of orthogonal polynomials직교다항식의 근의 분포

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 498
  • Download : 0
DC FieldValueLanguage
dc.contributor.advisorKwon, Kil-Hun-
dc.contributor.advisor권길헌-
dc.contributor.authorKim, Deok-Ho-
dc.contributor.author김덕호-
dc.date.accessioned2011-12-14T04:59:37Z-
dc.date.available2011-12-14T04:59:37Z-
dc.date.issued1995-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=98711&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/42398-
dc.description학위논문(석사) - 한국과학기술원 : 수학과, 1995.2, [ [ii], 20 p. ]-
dc.description.abstractIn [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.languageeng-
dc.publisher한국과학기술원-
dc.titleZero distribution of orthogonal polynomials-
dc.title.alternative직교다항식의 근의 분포-
dc.typeThesis(Master)-
dc.identifier.CNRN98711/325007-
dc.description.department한국과학기술원 : 수학과, -
dc.identifier.uid000933045-
dc.contributor.localauthorKwon, Kil-Hun-
dc.contributor.localauthor권길헌-
Appears in Collection
MA-Theses_Master(석사논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0