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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Why is the output of an LTI system the convolution of the input funtion and the impulse resp...

One way to approach this through the frequency domain. (Assume all the conditions about continuity of the system to make the following work.) Let $L$ denote the input-output operator. For each $f\in\m …
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