Math 6210 • Real Analysis

(a) State the definition of convolution \(*\) of two functions in
\(L^1(\mathbb R)\).

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(b) Prove directly that
\[
\lVert f*g\rVert_1\le \lVert f\rVert_1\lVert g\rVert_1
\]
Here, as usual, ``\(\lVert h\rVert_1\)'' denotes the \(L^1\) norm of function \(h\).

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