Cyclic elements of the shift operator in weighted anisotropic spaces of holomorphic functions in the polydisk |
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Authors: | F A Shamoyan |
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Institution: | (1) Bryansk State University, Russia |
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Abstract: | Let ϕ(r) = (ϕ1(r1), …, ϕn(rn)) be a vector-valued function on R
+
n
. A necessary and sufficient condition is obtained under which any function f ∈, H∞ (D
n
), f(z) ≠ 0, z ∈, D
n
, is cyclic in the corresponding weighted space Lp(ϕ), where D
n
is the unit polydisk in C
n. Bibliography: 13 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 226–234. |
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Keywords: | |
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