Weierstrass transform
= Weierstrass transform
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The <Weierstrass transform> is <Gaussian> <convolution>, $Wf(x)=(4\pi)^{-1/2}\int_{\mathbb R}e^{-(x-y)^2/4}f(y)\,dy$. It smooths appropriate functions and is the <heat semigroup> at unit time. The <Brownian transition semigroup> uses variance-$t$ Gaussian kernels and therefore supplies the scaled time family.