Abstract
We give an elementary proof of the well-known fact that shift-invariant operators onL 2[0, ∞) are represented by transfer functions which are bounded and analytic on the right open half-plane. We prove a generalization to Banach space-valuedL p-functions, where 1≤p<∞. We show that the result no longer holds forp=∞.
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This research was supported partially by the Weizmann Fellowship, and partially by the Air Force Office of Scientific Research under Contract F49620-86-C-0111.
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Weiss, G. Representation of shift-invariant operators onL 2 byH ∞ transfer functions: An elementary proof, a generalization toL p, and a counterexample forL ∞ . Math. Control Signal Systems 4, 193–203 (1991). https://doi.org/10.1007/BF02551266
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DOI: https://doi.org/10.1007/BF02551266