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Criteria for the existence of impulse responses and kernel representations for linear maps
Author(s) -
Ball David,
Sandberg Irwin W.
Publication year - 1990
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490180307
Subject(s) - impulse response , mathematics , impulse (physics) , real line , lti system theory , operator (biology) , kernel (algebra) , linear map , linear system , invariant (physics) , algebra over a field , pure mathematics , mathematical analysis , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , mathematical physics , gene
Results are given that establish, for the first time, necessary and sufficient conditions for the existence of impulse responses and kernel representations for linear not‐necessarily‐time‐invariant systems described by input‐output operator equations. These results concern systems whose inputs and outputs are real‐valued functions on the real line R , the half‐line 10, ∞) or R″′. They deal with causal as well as non‐causal maps and considerably extend related previous results which concern causal maps defined on functions on the half‐line.