Nevanlinna-Pick interpolation on Sobolev space
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- by Jim Agler PDF
- Proc. Amer. Math. Soc. 108 (1990), 341-351 Request permission
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
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R. Nevanlinna, Über Beschränkte Funktionen die in gegebene Punkten vorgeschriebene Werte annehmen, Ann. Acad. Sci. Fenn. Ser. A 13 (1), (1919), 1-71.
- Georg Pick, Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirkt werden, Math. Ann. 77 (1915), no. 1, 7–23 (German). MR 1511844, DOI 10.1007/BF01456817
- Donald Sarason, Generalized interpolation in $H^{\infty }$, Trans. Amer. Math. Soc. 127 (1967), 179–203. MR 208383, DOI 10.1090/S0002-9947-1967-0208383-8
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 341-351
- MSC: Primary 30E05; Secondary 46E35, 47B99
- DOI: https://doi.org/10.1090/S0002-9939-1990-0986645-2
- MathSciNet review: 986645