Manuscript XIX-E@1 · XIX-E.tex · section · 702f146e

Density multiplication and convolution do not coincide

Prescribed profiles, convolution, and clocks › Density multiplication and convolution do not coincide · lines 358–368

Let

(M_{σ} f) (t) = σ (t) f (t), (S_{ρ} f) (t) = \int_{R} ρ (u) f (t - u) d u,

where $ρ \in C_{c}^{\infty} (R)$ is nonnegative, has integral one, and is strictly positive near zero.

Displayed formulas in this passage

unlabeled · line 361
$(M_{σ} f) (t) = σ (t) f (t), (S_{ρ} f) (t) = \int_{R} ρ (u) f (t - u) d u,$