Pacific Journal of Mathematics

Extension of the theorems of Carathéodory-Toeplitz-Schur and Pick.

Sechiko Takahashi

Article information

Source
Pacific J. Math., Volume 138, Number 2 (1989), 391-399.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102650156

Mathematical Reviews number (MathSciNet)
MR996207

Zentralblatt MATH identifier
0631.30033

Subjects
Primary: 30E05: Moment problems, interpolation problems

Citation

Takahashi, Sechiko. Extension of the theorems of Carathéodory-Toeplitz-Schur and Pick. Pacific J. Math. 138 (1989), no. 2, 391--399. https://projecteuclid.org/euclid.pjm/1102650156


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References

  • [1] L. Ahlfors, Conformal Invariants. Topics in Geometric Function Theory, McGraw-Hill, New York, 1973.
  • [2] C. Caratheodory, Uber den Variabilittsbereich der Fourier'schen Konstan- ten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo, 32 (1911), 193-217.
  • [3] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
  • [4] D. E. Marshall, An elementary proof of Pick-Nevanlinna interpolation theo- rem, Michigan Math. J., 21 (1974), 219-223.
  • [5] G. Pick, Uber die Beschrnkungen analytischer Funktionen, welchedurch vorge- gebene Funktionswerte bewirkt werden,Math. Ann., 77 (1915), 7-23.
  • [6] J. Schur, Uber Potenzreihen, die im Innern des Einheitskreises beschrnkt sind, J. Reine Angew. Math., 147 (1917), 205-232.
  • [7] O. Toeplitz, Uberdie Fourier'scheEntwicklung positiver Funktionen, Rend. Circ. Mat. Palermo, 32 (1911), 191-192.