Nonnegative linearization of orthogonal polynomials

• Autorzy: Ryszard Szwarc
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 69
• Numer: 2
• Strony: 309-316

Daty

wydano

1996

otrzymano

1994-09-30

poprawiono

1995-04-07

Twórcy

autor

Ryszard Szwarc

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] R. Askey, Linearization of the product of orthogonal polynomials, in: Problems in Analysis (R. Gunning, ed.), Princeton University Press, Princeton, N.J., 1970, 223-228.
• [2] R. Askey and S. Wainger, A dual convolution structure for Jacobi polynomials, in: Proc. Conference on Orthogonal Expansions and their Continuous Analogues, D. Haimo (ed.), Southern Illinois University Press, Carbondale, 1967, 25-36.
• [3] R. Askey and J. A. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985).
• [4] T. Chihara, An Introduction to Orthogonal Polynomials, Math. Appl. 13, Gordon and Breach, New York, 1978.
• [5] J. Dougall, A theorem of Sonine in Bessel functions, with two extensions to spherical harmonics, Proc. Edinburgh Math. Soc. 37 (1919), 33-47.
• [6] G. Gasper, Linearization of the product of Jacobi polynomials. I, II, Canad. J. Math. 22 (1970), 171-175, 582-593.
• [7] H. Haddad, Chain sequence preserving linear transformations, Ann. Scuola Norm. Sup. Pisa (3) 24 (1970), 78-84.
• [8] S. Igari and Y. Uno, Banach algebras related to the Jacobi polynomials, Tôhoku Math. J. 21 (1969), 668-673.
• [9] L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318-343.
• [10] A. L. Schwartz, $l^1$-convolution algebras: representation and factorization, Z. Wahrsch. Verw. Gebiete 41 (1977), 161-176.
• [11] G. Szegö, Orthogonal Polynomials, Colloq. Publ. 23, Amer. Math. Soc., Providence, R.I., 4th ed., 1975.
• [12] R. Szwarc, Orthogonal polynomials and a discrete boundary value problem, I, SIAM J. Math. Anal. 23 (1992), 959-964.
• [13] R. Szwarc, Orthogonal polynomials and a discrete boundary value problem, II, ibid., 965-969.