Kernels of Toeplitz operators and rational interpolation
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 85-107
Cet article a éte moissonné depuis la source Math-Net.Ru
The kernel of a Toeplitz operator on the Hardy class $H^2$ in the unit disk is a nearly invariant subspace of the backward shift operator, and, by D. Hitt's result, it has the form $g\cdot K_\omega$, where $\omega$ is an inner function, $K_\omega=H^2\ominus\omega H^2$, and $g$ is an isometric multiplier on $K_\omega$. We describe the functions $\omega$ and $g$ for the kernel of the Toeplitz operator with symbol $\bar\theta\Delta$, where $\theta$ is an inner function and $\Delta$ is a finite Blaschke product.
@article{ZNSL_2018_467_a8,
author = {V. V. Kapustin},
title = {Kernels of {Toeplitz} operators and rational interpolation},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {85--107},
year = {2018},
volume = {467},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a8/}
}
V. V. Kapustin. Kernels of Toeplitz operators and rational interpolation. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 85-107. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a8/
[1] D. Hitt, “Invariant subspaces of $\mathcal H^2$ of an annulus”, Pacific J. Math., 134:1 (1988), 101–120 | DOI | MR | Zbl
[2] R. Nevanlinna, “Über beschränkte Funktionen, die in gegebenen Punkten vorgeschriebene Werte annehmen”, Ann. Acad. Sci. Fenn. Ser. A, 13 (1920), No. 1, 71 pp. | Zbl
[3] E. Hayashi, “Classification of nearly invariant subspaces of the backward shift”, Proc. Amer. Math. Soc., 110:2 (1990), 441–448 | DOI | MR | Zbl
[4] R. B. Crofoot, “Multipliers between invariant subspaces of the backward shift.”, Pacific J. Math., 166:2 (1994), 225–246 | DOI | MR | Zbl