Representation of Shift Invariant Operators on L2 by H at Infinity Transfer Functions: An Elementary Proof, a Generalization to L Rho and a Counterexample for L at Infinity

摘要

An elementary proof is given of the well known fact that shift invariant operators on (L-sq)/0, infinity) are represented by transfer functions which are bounded and analytic on the right open half-plane. Proved is a generalization to Banach space-valued L superscript p functions, where 1 < or = p < infinity. The result no longer holds for p = infinity. (JHD)