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Interpolating functions of minimal norm, star-invariant subspaces, and kernels of Toeplitz operators
Dyakonov, Konstantin M.
Universitat de Barcelona
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.
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
(c) American Mathematical Society (AMS), 1992
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Dyakonov, Konstantin M.; Nicolau, Artur