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1992-12

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/97261

Interpolating functions of minimal norm, star-invariant subspaces, and kernels of Toeplitz operators

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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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http://dx.doi.org/10.1090/S0002-9939-1992-1100649-2

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Funcions enteres, Funcions meromorfes, Funcions de variables complexes, Operadors lineals, Teoria d'operadors

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Entire functions, Meromorphic functions, Functions of complex variables, Linear operators, Operator theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

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DYAKONOV, Konstantin M. Interpolating functions of minimal norm, star-invariant subspaces, and kernels of Toeplitz operators. Proceedings of the American Mathematical Society. 1992. Vol. 116, num. 4, pags. 1007-1013. ISSN 0002-9939. [consulted: 16 of October of 2026]. Available at: https://hdl.handle.net/2445/97261

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