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Linear maps and impulse responses

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1 Author(s)
Sandberg, I.W. ; Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA

Several results are given concerning the representation of causal (mainly) linear operators defined on a set of locally integrable inputs. These results establish the existence of impulse responses and associated integral representations, as well as the convergence of a classical sum to an integral, in a general setting in which a certain continuity condition plays a central role. They also provide necessary and sufficient conditions for a causal linear operator to have a convolution representation with a continuous impulse-response function

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Circuits and Systems, IEEE Transactions on  (Volume:35 ,  Issue: 2 )