Summability of fourier orthogonal series for jacobi weight on a ball in ℝD

Transactions of the American Mathematical Society

Volumn 351, Issue 6, 1999, Pages 2439-2458

  Yuan, X U ^a  

^a UNIVERSITY OF OREGON   (United States)

Author keywords

Jacobi weight on the unit ball; Orthogonal polynomials in several variables; Positive sums; Summability

Indexed keywords

EID: 0000663047     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, 9th print, Dover Publ., New York, 1970.
2. R. Askey, Orthogonal polynomials and special functions, SIAM, Philadelphia, 1975. MR 58:1288
3. H. Berens and Y. Xu, Fejér means for multivariate Fourier series, Math. Z. 221 (1996), 449-465. MR 97a:42003
4. H. Berens and Y. Xu, ℓ - 1 summability for multiple Fourier integral, Approximation Theory VIII (C.K. Chui and L. Schumaker, ed.), vol. 2, World Sci. Publ. Co., 1995, pp. 55-62. MR 98e:42012
5. m, New Zealand J. Math. 23 (1994), 99-109. MR 95j:41047
6. A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, vol. 2, McGraw-Hill, New York, 1953. MR8h:33001b
7. G. Gasper, Positivity and the convolution structure for Jacobi series, Ann. of Math. 93 (1971), 112-118. MR 44:1852
8. G. Gasper, Positive sums of the classical orthogonal polynomials, SIAM J. Math. Anal. 8 (1977), 423-447. MR 55:5925
9. F. John, Plane waves and spherical means applied to partial differential equations, Wiley-Interscience, New York, 1955. MR 17:746d
10. Y. Kanjin, A convolution measure algebra on the unit disk, Tôhoku Math. J. 28 (1976), 105-115. MR 53:1178
11. T. Koormvinder, Two-variable analogues of the classical orthogonal polynomials, Theory and Application of Special Functions (R. A. Askey, ed.), Academic Press, New York, 1975, pp. 435-495. MR 53:5967
12. T. Koornwinder, The addition formula for Jacobi polynomials and spherical harmonics, SIAM J. Appl. Math. 25 (1973), 236-246. MR 49:10938
13. Szegö, G., Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Providence, RI, 1975. MR 51:8724
14. Y. Xu, On multivariate orthogonal polynomials, SIAM J. Math. Anal. 24 (1993), 783-794. MR 941:42031
15. Y. Xu, On orthogonal polynomials in several variables, Special functions, q-series, and related topics, Fields Institute Communications Series, vol. 14, 1997, pp. 247-270. MR 99a:33009
16. Y. Xu, Christoffel functions and Fourier series for multivariate orthogonal polynomials, J. Approx. Theory 82 (1995), 205-239. MR 96h:42021
17. A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, Cambridge, 1968. MR 38:4882