Zero sets and multiplier theorems for star-invariant sub spaces |
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Authors: | Konstantin M Dyakonov |
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Institution: | (1) St. Petersburg Branch (POMI), Steklov Institute of Mathematics, Fontanka 27, 191011 St. Petersburg, Russia |
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Abstract: | Given an inner function θ, let {Kskθ/p}:= Hp ∩θ {Hsk0/p} be the corresponding star-invariant subspace of the Hardy spaceH
p. We show that, unless θ is a finite Blaschke product, the zero sets for K
θ
p
-spaces are different for different p’s. We also investigate the (non)stability of zero sets when passing from {Kskθ/p} to {Ksku/q}, whereq > p and u is an inner function divisible by θ. This problem is motivated by the Beurling-Malliavin multiplier theorem for entire
functions, and we solve it (at least in a natural special case) by proving an appropriate multiplier theorem for K
θ
p
. |
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Keywords: | |
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