 Solution

ID: past-exam-of-the-functional-analysis-and-banach-and-c-algebras-course-of-the-university-of-oxford/2007/a/1/i/solution

The triangular kernel is nonnegative, has integral one, support in

[- δ, δ]

1/ δ

. Thus the convolution is defined at every point and

∣ (f * g) (t) ∣ \leq \int ∣ f (s) ∣ g (t - s) d s \leq ∥ f ∥_{1} / δ .

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