Weakly cyclic vectors with a given modulus
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 111-118
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Let $H^p$ be the Hardy space in the polydisc. Denote by $\mathcal P$ the set of all holomorphic polynomials. A vector $f\in H^p$ is called weakly cyclic if the product $f\mathcal P$ is weakly dense in $H^p$, $0. We construct weakly cyclic vectors with a prescribed lower semicontinuous modulus of the boundary values.
@article{ZNSL_2003_303_a5,
author = {E. Doubtsov},
title = {Weakly cyclic vectors with a~given modulus},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {111--118},
year = {2003},
volume = {303},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a5/}
}
E. Doubtsov. Weakly cyclic vectors with a given modulus. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 111-118. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a5/
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