Pacific Journal of Mathematics

On sieved orthogonal polynomials. IX. Orthogonality on the unit circle.

Mourad E. H. Ismail and Xin Li

Article information

Source
Pacific J. Math., Volume 153, Number 2 (1992), 289-297.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102635834

Mathematical Reviews number (MathSciNet)
MR1151563

Zentralblatt MATH identifier
0771.33007

Subjects
Primary: 42C05: Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]
Secondary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

Citation

Ismail, Mourad E. H.; Li, Xin. On sieved orthogonal polynomials. IX. Orthogonality on the unit circle. Pacific J. Math. 153 (1992), no. 2, 289--297. https://projecteuclid.org/euclid.pjm/1102635834


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References

  • [I] W. Al-Salam, W. Allaway and R. Askey, Sieved ultraspherical polynomials, Trans. Amer. Math. So, 284 (1984), 39-55.
  • [2] D. Bessis, Orthogonal polynomials, Pad approximation and Julia sets, in Or- thogonalPolynomials: Theory and Practice,edited by P. Nevai, Kluwer, Dor- drecht, (1990), 55-97.
  • [3] J. Charris and M. E. H. Ismail, On sieved orthogonal polynomials II: Random walk polynomials, Canad. J. Math., 38 (1986), 397-414.
  • [4] J. Charris and M. E. H. Ismail, On sieved orthogonal polynomials VII: Generalized polynomialmappings, Trans. Amer. Math. Soc, 330 (1991), to appear.
  • [5] T. S. Chihara, An Introductionto Orthogonal Polynomials,Gordon and Breach, New York, 1978.
  • [6] A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcen- dental Functions, volume 2, McGraw-Hill, New York, 1953.
  • [7] J. Geronimo and W. Van Assche, Orthogonal polynomials via polynomial map- pings, Trans. Amer. Math. Soc, 308 (1988), 559-581.
  • [8] Ya. L. Geronimus, OrthogonalPolynomials on a Circle and Interval,English translation, Pergamon Press, Oxford, 1960.
  • [9] U. Grenander and G. Szeg, Toeplitz Forms and TheirApplications, Chelsea, New York, 1986.
  • [10] M. E. H. Ismail, On sieved orthogonal polynomials III: Polynomials orthogonal on several intervals,Trans. Amer. Math. Soc, 294 (1986), 89-111.
  • [II] A. Mate, P. Nevai and V. Totik, Strong and weak convergence oforthogonal polynomials, Amer. J. Math., 109 (1987), 239-282.
  • [12] E. Rahmanov, Asymptotcs of the ratio of orthogonal polynomials, Math. USSR Sbornik, 32 (1977), 199-213.
  • [13] G. Szeg, Orthogonal Polynomials, Colloquium Publications, fourth edition, volume 23, American Mathematical Society, Providence, Rhode Island, 1975.
  • [14] W. Van Assche and A. Magnus, Sieved orthogonal polynomials and discrete measure withjumps dense in an interval,Proc. Amer. Math. Soc, 107 (1989), 163-173.

See also

  • Mourad E. H. Ismail. On sieved orthogonal polynomials. I. Symmetric Pollaczek analogues. I [MR 87a:33019] SIAM J. Math. Anal. 16 1985 5 1093--1113.
  • Jairo Charris, Mourad E. H. Ismail. On sieved orthogonal polynomials. {II}. Random walk polynomials. II [MR 87j:33014a] Canad. J. Math. 38 1986 2 397--415.
  • Mourad E. H. Ismail. On sieved orthogonal polynomials. {III}. Orthogonality on several intervals. III [MR 87j:33014b] Trans. Amer. Math. Soc. 294 1986 1 89--111.
  • Mourad E. H. Ismail. On sieved orthogonal polynomials. {IV}. Generating functions. IV [MR 87j:33014c] J. Approx. Theory 46 1986 3 284--296.
  • Jairo A. Charris, Mourad E. H. Ismail. On sieved orthogonal polynomials. V. Sieved Pollaczek polynomials. V [MR 88k:33017] SIAM J. Math. Anal. 18 1987 4 1177--1218.
  • Joaquin Bustoz, Mourad E. H. Ismail, Jet Wimp. On sieved orthogonal polynomials. {VI}. Differential equations. VI [MR 91a:33005] Differential Integral Equations 3 1990 4 757--766.
  • Jairo A. Charris, Mourad E. H. Ismail. Sieved orthogonal polynomials. {VII}. Generalized polynomial mappings. VII [MR 94a:33007] Trans. Amer. Math. Soc. 340 1993 1 71--93.
  • Nadhla A. Al-Salam, Mourad E. H. Ismail. On sieved orthogonal polynomials. {VIII}. Sieved associated Pollaczek polynomials. VIII [MR 93b:33004] J. Approx. Theory 68 1992 3 306--321.
  • X : Jairo A. Charris, Mourad E. H. Ismail, Sergio Monsalve. On sieved orthogonal polynomials. X. General blocks of recurrence relations. Pacific Journal of Mathematics volume 163, issue 2, (1994), pp. 237-267.