Nonnegative linearization of orthogonal polynomials

Ryszard Szwarc

Colloquium Mathematicae (1996)

  • Volume: 69, Issue: 2, page 309-316
  • ISSN: 0010-1354

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Szwarc, Ryszard. "Nonnegative linearization of orthogonal polynomials." Colloquium Mathematicae 69.2 (1996): 309-316. <http://eudml.org/doc/210345>.

@article{Szwarc1996,
author = {Szwarc, Ryszard},
journal = {Colloquium Mathematicae},
keywords = {positive linearization coefficients; third order linear differential equation; singular oscillators},
language = {eng},
number = {2},
pages = {309-316},
title = {Nonnegative linearization of orthogonal polynomials},
url = {http://eudml.org/doc/210345},
volume = {69},
year = {1996},
}

TY - JOUR
AU - Szwarc, Ryszard
TI - Nonnegative linearization of orthogonal polynomials
JO - Colloquium Mathematicae
PY - 1996
VL - 69
IS - 2
SP - 309
EP - 316
LA - eng
KW - positive linearization coefficients; third order linear differential equation; singular oscillators
UR - http://eudml.org/doc/210345
ER -

References

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  1. [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. [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. Zbl0174.36305
  3. [3] R. Askey and J. A. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985). Zbl0572.33012
  4. [4] T. Chihara, An Introduction to Orthogonal Polynomials, Math. Appl. 13, Gordon and Breach, New York, 1978. Zbl0389.33008
  5. [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. [6] G. Gasper, Linearization of the product of Jacobi polynomials. I, II, Canad. J. Math. 22 (1970), 171-175, 582-593. Zbl0191.35002
  7. [7] H. Haddad, Chain sequence preserving linear transformations, Ann. Scuola Norm. Sup. Pisa (3) 24 (1970), 78-84. Zbl0191.35304
  8. [8] S. Igari and Y. Uno, Banach algebras related to the Jacobi polynomials, Tôhoku Math. J. 21 (1969), 668-673. Zbl0192.48402
  9. [9] L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318-343. 
  10. [10] A. L. Schwartz, l 1 -convolution algebras: representation and factorization, Z. Wahrsch. Verw. Gebiete 41 (1977), 161-176. Zbl0357.43004
  11. [11] G. Szegö, Orthogonal Polynomials, Colloq. Publ. 23, Amer. Math. Soc., Providence, R.I., 4th ed., 1975. 
  12. [12] R. Szwarc, Orthogonal polynomials and a discrete boundary value problem, I, SIAM J. Math. Anal. 23 (1992), 959-964. Zbl0772.42013
  13. [13] R. Szwarc, Orthogonal polynomials and a discrete boundary value problem, II, ibid., 965-969. Zbl0772.42014

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