On the Cauchy transform and complex cubic splines


  • Crăciun Iancu “Babes-Bolyai” University, Cluj-Napoca, Romania
  • Tiberiu Oproiu “Babes-Bolyai” University, Cluj-Napoca, Romania
  • Alexandru Pop “Babes-Bolyai” University, Cluj-Napoca, Romania
  • Vasile Pop Cluj-Napoca, Romania




Cauchy transform, Hölder condition, complex cubic spline
Abstract views: 234


In this paper we approximate the Cauchy transform of a complex function on a simple closed curve, using an interpolation cubic spline function given by Iancu (1987).


Download data is not yet available.


Ahlberg, J. H., Nilson, E. N. and Walsh, J. L., Complex cubic splines, Trans. Amer. Math. Soc., 129, pp. 391-413, 1967, https://doi.org/10.1090/S0002-9947-1967-0217484-X. DOI: https://doi.org/10.1090/S0002-9947-1967-0217484-X

Atkinson, K. E., The numerical solution of Fredholm integral equations of the second kind, SIAM J. Numer. Anal., 4, pp. 337-348, 1967, https://doi.org/10.1137/0704029. DOI: https://doi.org/10.1137/0704029

Atkinson, K. E., The numerical evaluation of the Cauchy transform on simple closed curves, SIAM J. Numer. Anal., 9, pp. 284-299, 1972, https://doi.org/10.1137/0709028. DOI: https://doi.org/10.1137/0709028

Atteia, M., Fage, C. and Gages, J., Etude et convergence des fonctions spline complexe, R.A.I.R.O. Analyse numerique, 18, no. 3, pp. 391-413, 1984. DOI: https://doi.org/10.1051/m2an/1984180302191

Chen Hanlin, Complex Spline Functions, Scientia Sinica, XXIV, no. 2, pp. 160-169, 1981.

Chien-Ke Lu, The Approximation of Cauhy-Type Integrals by some kinds of Interpolatory Splines, J. Approx. Theory, 36, pp. 197-212, 1982, https://doi.org/10.1016/0021-9045(82)90040-5. DOI: https://doi.org/10.1016/0021-9045(82)90040-5

Davis, P. J. and Rabinowitz, P., Numerical Integration Blaisdell, Waltham, Mass., 1967.

Gakhow, F. D., boundary Value Problem, Addison-Wesley, Reading, Mass., 1966. DOI: https://doi.org/10.1016/B978-0-08-010067-8.50007-4

Iancu, C., Sur une fonctions spline cubique complexe, "Babeş-Bolyai" Univ. Seminar on Numerical and Statistical Calculus, Preprint nr. 9, pp. 73-84, 1987.

Iancu, C., the error analysis in interpolation by complex spline fucntions, Studia Univ. "Babeş-Bolyai" Mathematica, XXXIV, no. 1, pp. 71-76, 1989.

Muskhelishvilli, N. I., Singular Integral Equations, Noordhoff, Groningen, Holand, 1953.

Stewart, C. E., On the Numerical Evaluation of Singular Integrals of Cauchy Type, J. Soc. Indust. Appl. Math., 8, no. 2, pp. 343-353, 1960, https://doi.org/10.1137/0108021. DOI: https://doi.org/10.1137/0108021




How to Cite

Iancu, C., Oproiu, T., Pop, A., & Pop, V. (2003). On the Cauchy transform and complex cubic splines. Rev. Anal. Numér. Théor. Approx., 32(1), 63–68. https://doi.org/10.33993/jnaat321-734