Diagonalization of Certain Integral Operators II ∗

@inproceedings{Ismail1996DiagonalizationOC,
  title={Diagonalization of Certain Integral Operators II ∗},
  author={Mourad E. H. Ismail and Mizan Rahman and Ruiming Zhang},
  year={1996}
}
We establish an integral representations of a right inverses of the Askey-Wilson finite difference operator in an L2 space weighted by the weight function of the continuous q-Jacobi polynomials. We characterize the eigenvalues of this integral operator and prove a q-analog of the expansion of eixy in Jacobi polynomials of argument x. We also outline a general procedure of finding integral representations for inverses of linear operators. Running title: Integral Operators 1990 Mathematics… CONTINUE READING
Highly Cited
This paper has 46 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
24 Citations
19 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 19 references

Contiguous relations

  • D. P. Gupta, M.E.H. Ismail, D. R. Masson
  • basic hypergeometric series and orthogonal…
  • 1992
Highly Influential
6 Excerpts

Some basic hypergeometric polynomials that generalize Jacobi polynomials

  • R. Askey, J. Wilson
  • Memoires Amer. Math. Soc. Number 319
  • 1985
Highly Influential
5 Excerpts

Asymptotic and generating relations for q-Jacobi and 4φ3 polynomials

  • M.E.H. Ismail, J. Wilson
  • J. Approximation Theory 36
  • 1982
Highly Influential
10 Excerpts

Continued Fraction: Analytic Theory and Applications

  • W. B. Jones, W. Thron
  • Addison Wesley, Reading, Massachusetts
  • 1980
Highly Influential
5 Excerpts

A class of continued fractions

  • H. M. Schwartz
  • Duke Math. J. 6
  • 1940
Highly Influential
6 Excerpts

Characterization theorems for orthogonal polynomials

  • W. Al-Salam
  • “Orthogonal Polynomials: Theory and Practice”, P…
  • 1989

Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials

  • A. P. Magnus
  • “Orthogonal Polynomials and Their Applications…
  • 1988
1 Excerpt

Some explicit Padé approximants for the function φ/φ and a related quadrature formula involving Bessel functions

  • J. Wimp
  • SIAM J. Math. Anal. 16
  • 1985
2 Excerpts

A generalization of ultraspherical polynomials

  • R. Askey, M.E.H. Ismail
  • “Studies in Pure Mathematics”, P. Erdös ed…
  • 1983

The zeros of basic Bessel functions

  • M.E.H. Ismail
  • the functions Jv+ax(x), and associated orthogonal…
  • 1982

Similar Papers

Loading similar papers…