Causality Structure and the Weierstrass Theorem.
MICHIGAN UNIV ANN ARBOR SYSTEMS ENGINEERING LAB
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In a recent paper P. M. Prenter has shown that the Weierstrass theorem can be lifted up to a real separable Hilbert space, H. In this paper H is equipped with an identity resolving orthoprojector chain. The Weierstrass type result of Prenter namely if f is any continuous function on H, then there exists a finite order approximating polynomic operator on every compact K belongs to H, is sharpened by the extension if f is strictly causal strictly anticausal then the polynomic approximation can also be strictly causal strictly anticausal. Other extensions in the same spirit are developed and the results are interpreted in the setting of Volterra operators on L sub 2. Author
- Theoretical Mathematics