|
Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 107, Pages 104–135
(Mi znsl3418)
|
|
|
|
Sets of simply-invariance
N. G. Makarov
Abstract:
Let $X$ be a space of smooth functions on the unit circle $\mathbb T$. Suppose that the operator of multiplication by $z$ is invertible on $X$. A closed set $E$, $E\subset\mathbb T$, is (by definition) the set of simply-invariance for the space $X$ if there exists a function $f$, $f\in X$, such that $f|_E\equiv0$ and
$z^{-1}\not\in\operatorname{span}\{z^nf:n\ge0\}$, It is proved that the class of sets of simply-invariance for the spaces $C^n$, $W_p^n$ ($p<\infty$), $\lambda_\omega^n$, coincides with the class of sets of zero Lebesgue measure, for the space $C^\infty$, with the class of Carleson sets, for the space $\Lambda_\omega^n$ with the class of all nowhere dense closed sets. Some related problems are also considered.
Citation:
N. G. Makarov, “Sets of simply-invariance”, Investigations on linear operators and function theory. Part X, Zap. Nauchn. Sem. LOMI, 107, "Nauka", Leningrad. Otdel., Leningrad, 1982, 104–135; J. Soviet Math., 36:3 (1987), 363–382
Linking options:
https://www.mathnet.ru/eng/znsl3418 https://www.mathnet.ru/eng/znsl/v107/p104
|
Statistics & downloads: |
Abstract page: | 142 | Full-text PDF : | 90 |
|