Orthogonal polynomial solutions of linear ordinary differential equations. (English) Zbl 0993.33004
This survey paper recapitulates the results obtained during the last decade on orthogonal polynomials. The material dwells on one hundred references whose three quarters have been published in that period. First they reveal the pertinent terminology and new definitions. Then they discuss various extensions and gereralizations such as: i) Bochner-Krall class of polynomial systems, ii) Moment functional differential equations, iii) Polynomial systems which are orthogonal with respect to weight distributions, iv) Classification of the differential equations satisfied by orthogonal polynomial systems, v) Sobolev orthogonal polynomials. Finally, they point out some open problems as well as conjectures belonging to intersection of orthogonal polynomials, differential equations, distribution theory, and functional analysis. Some new applications of orthogonal polynomiais in mathematics, physics, and engineering are also discussed.
Reviewer: Mithat Idemen (İstanbul)
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |
Keywords:
Sobolev orthogonal polynomialsReferences:
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