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Title: Interpolating functions of minimal norm, star-invariant subspaces, and kernels of Toeplitz operators
Author: Dyakonov, Konstantin M.
Keywords: Funcions enteres
Funcions meromorfes
Funcions de variables complexes
Operadors lineals
Teoria d'operadors
Entire functions
Meromorphic functions
Functions of complex variables
Linear operators
Operator theory
Issue Date: Dec-1992
Publisher: American Mathematical Society (AMS)
Abstract: It is proved that for each inner function $ \theta $ there exists an interpolating sequence $ \left\{ {{z_n}} \right\}$ in the disk such that $ {\sup _n}\vert\theta ({z_n})\vert < 1$, but every function $ g$ in $ {H^\infty }$ with $ g({z_n}) = \theta ({z_n})(n = 1,2, \ldots )$ satisfies $ \vert\vert g\vert{\vert _\infty } \geq 1$. Some results are obtained concerning interpolation in the star-invariant subspace $ {H^2} \ominus \theta {H^2}$. This paper also contains a 'geometric' result connected with kernels of Toeplitz operators.
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It is part of: Proceedings of the American Mathematical Society, 1992, vol. 116, num. 4, p. 1007-1013
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ISSN: 0002-9939
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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