Sobolev orthogonal polynomials and spectral differential equations

Authors:
I. H. Jung, K. H. Kwon, D. W. Lee and L. L. Littlejohn

Journal:
Trans. Amer. Math. Soc. **347** (1995), 3629-3643

MSC:
Primary 34L05; Secondary 33C45

MathSciNet review:
1308015

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We find necessary and sufficient conditions for a spectral differential equation

**[1]**R. P. Boas Jr.,*The Stieltjes moment problem for functions of bounded variation*, Bull. Amer. Math. Soc.**45**(1939), no. 6, 399–404. MR**1563993**, 10.1090/S0002-9904-1939-06992-9**[2]**Antonio J. Duran,*The Stieltjes moments problem for rapidly decreasing functions*, Proc. Amer. Math. Soc.**107**(1989), no. 3, 731–741. MR**984787**, 10.1090/S0002-9939-1989-0984787-0**[3]**R. Koekoek,*The search for differential equations for orthogonal polynomials by using computers*, Delft University of Technology, Report no. 91-55, 1991.**[4]**Roelof Koekoek,*The search for differential equations for certain sets of orthogonal polynomials*, Proceedings of the Seventh Spanish Symposium on Orthogonal Polynomials and Applications (VII SPOA) (Granada, 1991), 1993, pp. 111–119. MR**1256017**, 10.1016/0377-0427(93)90141-W**[5]**R. Koekoek and H. G. Meijer,*A generalization of Laguerre polynomials*, SIAM J. Math. Anal.**24**(1993), no. 3, 768–782. MR**1215437**, 10.1137/0524047**[6]**H. L. Krall,*Certain differential equations for Tchebycheff polynomials*, Duke Math. J.**4**(1938), no. 4, 705–718. MR**1546091**, 10.1215/S0012-7094-38-00462-4**[7]**H. L. Krall,*On orthogonal polynomials satisfying a certain fourth order differential equation*, Pennsylvania State College Studies,**1940**(1940), no. 6, 24. MR**0002679****[8]**H. L. Krall and I. M. Sheffer,*Differential equations of infinite order for orthogonal polynomials*, Ann. Mat. Pura Appl. (4)**74**(1966), 135–172. MR**0206441****[9]**K. H. Kwon and L. L. Littlejohn,*Classification of Sobolev orthogonal polynomials satisfying second order differential equations*, RIM-GARC Preprint series 93-26, Seoul National Univ., 1933.**[10]**K. H. Kwon, L. L. Littlejohn, and B. H. Yoo,*Characterizations of orthogonal polynomials satisfying differential equations*, SIAM J. Math. Anal.**25**(1994), no. 3, 976–990. MR**1271321**, 10.1137/S0036141092236437**[11]**Lance L. Littlejohn and David Race,*Symmetric and symmetrisable differential expressions*, Proc. London Math. Soc. (3)**60**(1990), no. 2, 344–364. MR**1031457**, 10.1112/plms/s3-60.2.344

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
34L05,
33C45

Retrieve articles in all journals with MSC: 34L05, 33C45

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1995-1308015-9

Keywords:
Sobolev orthogonal polynomials,
Sobolev bilinear forms,
spectral differential equations

Article copyright:
© Copyright 1995
American Mathematical Society