Pacific Journal of Mathematics

Total positivity and reproducing kernels.

Jacob Burbea

Article information

Source
Pacific J. Math., Volume 55, Number 2 (1974), 343-359.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102910971

Mathematical Reviews number (MathSciNet)
MR0584956

Zentralblatt MATH identifier
0301.30006

Subjects
Primary: 30A31
Secondary: 41A55: Approximate quadratures 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Citation

Burbea, Jacob. Total positivity and reproducing kernels. Pacific J. Math. 55 (1974), no. 2, 343--359. https://projecteuclid.org/euclid.pjm/1102910971


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References

  • [1] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc, 68 (1950), 337-404.
  • [2] S. Bergman, The Kernel Function and ConformalMapping, Amer. Math. Soc, Math. Surveys 5, Providence, R. I., 1970.
  • [3] L. de Branges, Hilbert Spaces of EntireFunctions,Prentice-Hall, Englewood Cliffs, N. J., 1968.
  • [4] J. Burbea, On the Gaussian curvature related to the Szego metric, (to appear).
  • [5] P. J. Davis, Interpolationand Approximation,Blaisdell, Waltham, Mass., 1963.
  • [6] S. Karlin, Total Positivity,Vol. 1, Stanford Univ. Press, Stanford, Cal., 1968.
  • [7] S. Karlin, Best quadrature formulas and splines, J. Approximation Theory, 4 (1971), 59-90.
  • [8] N. Richter-Dyn, Properties of minimalintegrationrules, II, SIAM J. Numer. Anal., 8 (1971), 497-508.