Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The uniform continuity of certain translation semigroups


Author: Jimmie Lee Johnson
Journal: Proc. Amer. Math. Soc. 71 (1978), 197-203
MSC: Primary 47D05; Secondary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1978-0512908-5
MathSciNet review: 0512908
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {S_h}f(x) = f(x + h)$ for $ h \geqslant 0$, for $ f \in {L^2}({R^ + };K)$, where K is a separable Hilbert space. The translation semigroup $ {S_h}$ when restricted to an invariant subspace L is uniformly continuous if and only if $ {G_L}$ is an inner function and has an analytic continuation across an open arc of the unit circle at $ z = 1$. The operator-valued function $ {G_L}$ is associated with the invariant subspace L by Beurling's theorem.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D05, 47A15

Retrieve articles in all journals with MSC: 47D05, 47A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0512908-5
Keywords: Invariant subspace, semigroup of operators, Hardy spaces, Fourier transform, inner function, unilateral shift
Article copyright: © Copyright 1978 American Mathematical Society