Representation of shift-invariant operators onL
2 byH
∞ transfer functions: An elementary proof,a generalization toL
p,and a counterexample forL
∞ |
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Authors: | George Weiss |
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Affiliation: | (1) Department of Mathematics, Virginia Tech, 24061 Blacksburg, Virginia, U.S.A. |
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Abstract: | We give an elementary proof of the well-known fact that shift-invariant operators onL
20, ∞) 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=∞.
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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Keywords: | Shift-invariant operator Transfer function Linear systems |
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