On the representation of shift-invariant operators by transfer functions

摘要

We give simple sufficient conditions on a function space on (0, infinity) to ensure that all shift-invariant operators defined on it are represented by transfer functions. This enables us to extend the result of Weiss on L-p(0, infinity) for 1 less than or equal to p < infinity (but not p = infinity) to more general situations. (C) 1998 Elsevier Science B.V. All rights reserved. [References: 8]