DC Field | Value | Language |
---|---|---|
dc.contributor.author | Jung, IH | ko |
dc.contributor.author | Kwon, Kil Hyun | ko |
dc.contributor.author | Yoon, GJ | ko |
dc.date.accessioned | 2013-03-02T21:48:44Z | - |
dc.date.available | 2013-03-02T21:48:44Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 1997-02 | - |
dc.identifier.citation | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.78, no.2, pp.277 - 293 | - |
dc.identifier.issn | 0377-0427 | - |
dc.identifier.uri | http://hdl.handle.net/10203/75702 | - |
dc.description.abstract | Assume that {P-n(x)}(infinity)(n=0) are orthogonal polynomials relative to a quasi-definite moment functional sigma, which satisfy a differential equation of spectral type of order D (2 less than or equal to D less than or equal to infinity): L(D)[y](x) = (i=1)Sigma(D) li(x)y((i))(x) = lambda(n)y(x), where l(i)(x) are polynomials of degree less than or equal to i. Let phi be the symmetric bilinear form of discrete Sobolev type defined by phi(p,q) = (sigma,pq) + Np-(k)(c)q((k))(c), where N(not equal 0) and c are real constants, k is a non-negative integer, and p and q are polynomials. We first give a necessary and sufficient condition for phi to be quasi-definite and then show: If phi is quasi-definite, then the corresponding Sobolev-type orthogonal polynomials {R(n)(N,k;c)(x)}(infinity)(n=0) satisfy a differential equation of infinite order of the form N{a(0)(x,n)y(x) + (i=1)Sigma(infinity)a(i)(x)y((i))(x)} + L(D)[y](x) = lambda(n)y(x), where {a(i)(x)}(infinity)(i=0) are polynomials of degree less than or equal to i, independent of n except a(0)(x) := a(0)(x,n). We also discuss conditions under which such a differential equation is of finite order when a is positive-definite, D < infinity, N greater than or equal to 0, and k = 0. | - |
dc.language | English | - |
dc.publisher | ELSEVIER SCIENCE BV | - |
dc.subject | GENERALIZED LAGUERRE-POLYNOMIALS | - |
dc.subject | SETS | - |
dc.title | Differential equations of infinite order for Sobolev-type orthogonal polynomials | - |
dc.type | Article | - |
dc.identifier.wosid | A1997WK94300005 | - |
dc.identifier.scopusid | 2-s2.0-0031077710 | - |
dc.type.rims | ART | - |
dc.citation.volume | 78 | - |
dc.citation.issue | 2 | - |
dc.citation.beginningpage | 277 | - |
dc.citation.endingpage | 293 | - |
dc.citation.publicationname | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | - |
dc.contributor.localauthor | Kwon, Kil Hyun | - |
dc.contributor.nonIdAuthor | Jung, IH | - |
dc.contributor.nonIdAuthor | Yoon, GJ | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Sobolev-type orthogonal polynomials | - |
dc.subject.keywordAuthor | differential equations of spectral type | - |
dc.subject.keywordPlus | GENERALIZED LAGUERRE-POLYNOMIALS | - |
dc.subject.keywordPlus | SETS | - |
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