Criteria for the existence of impulse responses and kernel representations for linear maps

✍ Scribed by David Ball; Irwin W. Sandberg

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 653 KB
• Volume: 18
• Category: Article
• ISSN: 0098-9886
• DOI: 10.1002/cta.4490180307

✦ Synopsis

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 [ 0 , ~) 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.