Lp distributions: analysis by impulse response and convolution

Abstract

In this paper it is shown that every continuous LTI (linear time-invariant) system L defined either on L or on D Lp (1 6 p 6 ∞) admits an impulse response ∆ ∈ D Lp′ (1 6 p ′ 6 ∞, 1/p+ 1/p′ = 1). Schwartz’ extension to D Lp distributions of the usual notion of convolution product for L functions is used to prove that (apart some restrictions for p =∞) for every f either in L or in D Lp we have L (f) = ∆ ∗ f . Perspectives of applications to linear differential equations are shown by one example.

Cite this paper

@inproceedings{Ciampa2008LpDA, title={Lp distributions: analysis by impulse response and convolution}, author={Maurizio Ciampa and Marco Franciosi and Mario Poletti}, year={2008} }