Classification of classical orthogonal polynomials

Journal of the Korean Mathematical Society

Volumn 34, Issue 4, 1997, Pages 973-1006

  Kwon, Kil H ^a   Littlejohn, Lance L ^b  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b UTAH STATE UNIVERSITY   (United States)

Author keywords

Classical orthogonal polynomials; Second order differential equations

Indexed keywords

EID: 0003264538     PISSN: 03049914     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. J. Aczél, Eine Bemerkung über die Characterisierung der klassischen orthogonale Polynome, Acta Math. Sci. Hung. 4 (1953), 315-321.
2. R. P. Boas, The Stieltjes moment problem for functions of bounded variation, Bull. Amer. Math. Soc. 45 (1939), 399-404.
3. S. Bochner, Über Sturm-Liouvillesche Polynomsysteme, Math. Z. 29 (1929), 730-736.
4. T. S. Chihara, An introduction to orthogonal polynomials, Gordon and Breach, New York, 1977.
5. C. W. Cryer, Rodrigues' formulas and the classical orthogonal polynomials, Boll. Unione Mat. Ital. 25 (1970), 1-11.
6. Á. Császár, Sur les polynômes orthogonaux classiques, Annales Univ. Sci. Budapest Sec. Math. 1 (1958), 33-39.
7. A. J. Duran, The Stieltjes moment problem for rapidly decreasing functions, Proc. Amer. Math. Soc. 107(3) (1989), 731-741.
8. -, Functions with given moments and weight functions for orthogonal polynomials, Rocky Mountain J. Math. 23(1) (1993), 87-104.
9. W. D. Evans, W. N. Everitt, K. H. Kwon, and L. L. Littlejohn, Real orthogonalizing weights for Bessel polynomials, J. Comp. Appl. Math. 49 (1993), 51-57.
10. J. Favard, Sur les polynomes de Tchebicheff, C.R. Acad. Sci. Paris 200 (1935), 2052-2053.
11. J. Feldmann, On a characterization of classical orthogonal polynomials, Acta. Sc. Math. 17(1956), 129-133.
12. G. H. Hardy, On Stieltjes' "Probleme des Moments", Messenger of Math. 4(1917), 175-182.
13. L. Hörmander, The analysis of linear partial differential operators I, Springer-Verlag, New York, 1983.
14. S. S. Kim and K. H. Kwon, Hyperfunctional weights for orthogonal polynomials, Results in Math. 18 (1990), 273-281.
15. -, Generalized weights for orthogonal polynomials, Diff. and Int. Equations 4(1991), 601-608.
16. A. M. Krall and L. L. Littlejohn, On the classification of differential equations having orthogonal polynomial solutions II, Ann. Mat. Pura Appl. 4 (1987), 77-102.
17. H. L. Krall, Certain differential equations for Tchebychev polynomials, Duke Math. J. 4 (1938), 705-719.
18. -, On derivatives of orthogonal polynomials II, Bull. Amer. Math. Soc. 47 (1941), 261-264.
19. H. L. Krall and O. Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100-115.
20. H. L. Krall and I. M. Sheffer, A characterization of orthogonal polynomials, J. Math. Anal. Appl. 8 (1964), 232-244.
21. -, Differential equations of infinite order for orthogonal polynomials, Ann. Mat. Pura Appl. 4 (1966), 135-172.
22. K. H. Kwon, S. S. Kim, and S. S. Han, Orthogonalizing weights for Tchebychev sets of polynomials, Bull. London Math. Soc. 24 (1992), 361-367.
23. K. H. Kwon, J. K. Lee, and B. H. Yoo, Characterizations of classical orthogonal polynomials, Results in Math. 24 (1993), 119-128.
24. K. H. Kwon and L. L. Littlejohn, Sobolev orthogonal polynomials and second-order differential equations, Rocky Mt. J. Math. (to appear).
25. K. H. Kwon, L. L. Littlejohn, and B. H. Yoo, Characterizations of orthogonal polynomials satisfying differential equations, SIAM J. Math. Anal. 25(3) (1994), 976-990.
26. -x dx, Bull. de la Socíeté Math., de France 7 (1879), 72-81.
27. P. Lesky, Die Charakterisierung der klassischen orthogonalen Polynome durch Sturm-Liouvillesche Differentialgleichungen, Arch. Rat. Mech. Anal. 10 (1962), 341-352.
28. L. L. Littlejohn, On the classification of differential equations having orthogonal polynomial solutions, Ann. Mat. Pura Appl. 4 (1984), 35-53.
29. L. L. Littlejohn and D. Race, Symmetric and symmetrisable ordinary differential expressions, Proc. London Math. Soc. 1 (1990), 334-356.
30. P. Maroni, An integral representation for the Bessel form, J. Comp. Appl. Math. 57 (1995), 251-260.
31. M. Mikolás, Common characterization of the Jacobi, Laguerre and Hermite-like polynomials (in Hungarian), Mate. Lapok 7 (1956), 238-248.
32. R. D. Morton and A. M. Krall, Distributional weight functions for orthogonal polynomials, SIAM J. Math. Anal. 9(4) (1978), 604-626.
33. M. V. Romanovski, Sur quelques classes nouvelle de polynomes orthogonaux, C.R. Acad. Sci. Paris 188 (1929), 1023-1025.
34. N. J. Sonine, Recherches sur les fonctions cylindriques et le développment des fonctions continues en series, Math. Ann. 16 (1880), 1-80.
35. T. J. Stieltjes, Recherches sur les fractions continues, Ann. de la Faculté des Sci. de Toulouse 8 (1894), J1-122;
36. Ann. de la Faculté des Sci. de Toulouse 9 (1895), A1-47;
37. Oeuvres 2, 398-566.