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Continuous LTI Systems Defined on L^{p} Functions and {cal D}_{L^{p}}^{\prime } Distributions: Analysis by Impulse Response and Convolution

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3 Author(s)
Ciampa, M. ; Dept. of Appl. Math., Univ. of Pisa, Pisa ; Franciosi, M. ; Poletti, M.

In this paper, it is shown that every continuous linear time-invariant system L defined either on L p or on D'L p (1lesplesinfin) admits an impulse response DeltaisinD'L p' (1lesp'lesinfin, 1/p+1/p'=1). Schwartz' extension to D'L p distributions of the usual notion of convolution product for L p functions is used to prove that (apart from some restrictions for p=infin), for every f either in L p or in D'L p, we have L(f)=Delta*f. Perspectives of applications to linear differential equations are shown by one example.

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:55 ,  Issue: 6 )