Abstract
AbstractThe translation operator is bounded in the Paley–Wiener spaces and, more generally, in the Bernstein spaces. The goal of this paper is to find some necessary conditions for the boundedness of the translation operator in the de Branges spaces, of which the Paley–Wiener spaces are special cases. Indeed, if the vertical translation operator $$T_\tau $$
T
τ
defined on the de Branges space $${\mathcal H}(E)$$
H
(
E
)
is bounded, then a suitably defined measure $$d\mu (z)$$
d
μ
(
z
)
is a Carleson measure for the associated model space $$K(\Theta )$$
K
(
Θ
)
. This relation allows us to state necessary conditions for the boundedness of the vertical translation $$T_\tau $$
T
τ
. Finally, similar results are also obtained for the horizontal translation $$T_\sigma $$
T
σ
.
Funder
Università degli Studi di Milano
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics
Reference15 articles.
1. Aleksandrov, A.B.: A simple proof of a theorem of Vol’berg and Treil’ on the embedding of coinvariant subspaces of the shift operator. J. Math. Sci. 85, 1773–1778 (1997)
2. Baranov, A.D.: Differentiation in the Branges spaces and embedding theorems. J. Math. Sci. 101, 2881–2913 (2000)
3. Baranov, A.D.: Bernstein’s inequality in the de Branges spaces and embedding theorems. Am. Math. Soc. Transl. 209, 21–49 (2003)
4. Baranov, A.D.: Estimate of the $$L^p-$$norms of derivatives in spaces of entire functions. J. Math. Sci. 129, 3927–3943 (2005)
5. de Branges, L.: Hilbert Spaces of Entire Functions. Prentice Hall, Englewood Cliffs (1968)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献