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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Nevanlinna-Pick interpolation on Sobolev space

Author: Jim Agler
Journal: Proc. Amer. Math. Soc. 108 (1990), 341-351
MSC: Primary 30E05; Secondary 46E35, 47B99
MathSciNet review: 986645
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Abstract: In this paper we shall prove an analog of the classical result of Nevanlinna and Pick concerning the bound of holomorphic functions on the unit disc that take prescribed values at prescribed points with the role that the classical Hardy space of analytic functions with square integrable power series plays in the modern operator-theoretic formulation of that result instead played by a Sobolev space of complex functions on the interval $ [0,1]$ whose derivatives are in $ {L^2}\left( {0,1} \right)$.

References [Enhancements On Off] (What's this?)

  • [1] R. Nevanlinna, Über Beschränkte Funktionen die in gegebene Punkten vorgeschriebene Werte annehmen, Ann. Acad. Sci. Fenn. Ser. A 13 (1), (1919), 1-71.
  • [2] G. Pick, Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirkt werden, Math. Ann. 77 (1916), 7-23. MR 1511844
  • [3] D. Sarason, Generalized interpolation in $ {H^\infty }$, Trans. Amer. Math. Soc. 127 (1967), 179-203. MR 0208383 (34:8193)

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Article copyright: © Copyright 1990 American Mathematical Society

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