Lp distributions: analysis by impulse response and convolution
نویسندگان
چکیده
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.
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