Partial differential equations having orthogonal polynomial solutions

Kim, Y. J.; Kwon, Kil Hyun; Lee, J. K.

doi:10.1016/s0377-0427(98)00160-5

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction3

Definition1

Orthogonal Polynomials In Two Variables1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1999

2018

Publication Types

Select...

Article8

Relationship

Self Cite0

Independent8

Authors

Journals

Cited by 18 publications

(32 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If s = 0, that is, deg = p 2 and deg = 1, we recover the definition of classical WOPS given in [5], which includes the classical bivariate orthogonal polynomials studied by Krall and Sheffer [13], and other authors [3,8,9,14,16].…”

Section: Definitionmentioning

confidence: 99%

A semiclassical perspective on multivariate orthogonal polynomials

Morales

Fernández

Pérez

et al. 2008

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

Section: Definitionmentioning

confidence: 99%

A semiclassical perspective on multivariate orthogonal polynomials

Morales

Fernández

Pérez

et al. 2008

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…For an exhaustive description of this and other related subjects see, for instance, [11][12][13][14][15]9,16,17].…”

Section: Orthogonal Polynomials In Two Variablesmentioning

confidence: 99%

New steps on Sobolev orthogonality in two variables

Bracciali

Delgado

Fernández

et al. 2010

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

MSC: 42C05 33C50Keywords: Orthogonal polynomials in two variables Sobolev orthogonal polynomials Classical orthogonal polynomials a b s t r a c t Sobolev orthogonal polynomials in two variables are defined via inner products involving gradients. Such a kind of inner product appears in connection with several physical and technical problems. Matrix second-order partial differential equations satisfied by Sobolev orthogonal polynomials are studied. In particular, we explore the connection between the coefficients of the second-order partial differential operator and the moment functionals defining the Sobolev inner product. Finally, some old and new examples are given.

show abstract

“…In fact, [8] is the starting point to prove results for orthogonal polynomials in several variables similar to the standard properties for one-variable orthogonal polynomials (see [3,5,6,15]). …”

Section: Introductionmentioning

confidence: 99%