Interpolating functions of minimal norm, star-invariant subspaces and kernels of Toeplitz operators
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- by Konstantin M. Dyakonov PDF
- Proc. Amer. Math. Soc. 116 (1992), 1007-1013 Request permission
Abstract:
It is proved that for each inner function $\theta$ there exists an interpolating sequence $\left \{ {{z_n}} \right \}$ in the disk such that ${\sup _n}|\theta ({z_n})| < 1$, but every function $g$ in ${H^\infty }$ with $g({z_n}) = \theta ({z_n})(n = 1,2, \ldots )$ satisfies $||g|{|_\infty } \geq 1$. 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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 1007-1013
- MSC: Primary 30D55; Secondary 30E05, 47B35
- DOI: https://doi.org/10.1090/S0002-9939-1992-1100649-2
- MathSciNet review: 1100649