Notes on the superposition scandal

Authors:
Irwin W. Sandberg
Affiliations:
Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas
Venue:
MACMESE'07 Proceedings of the 9th WSEAS international conference on Mathematical and computational methods in science and engineering
Year:
2007

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Abstract

Attention is focused on continuous-space shift-invariant systems with continuous system maps and inputs and outputs that are elements of L∞(Rd). It is shown that infinite superposition can fail in this important setting. It is also shown that continuous shift-invariant linear mappings need not commute with the operation of integration (even when the two composite operations are well defined).