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

2 votes
1 answer
107 views

Lower bounds on translates of a function over a compact set

Let $f\in L^p(\mathbb{R})$ and define $f_\theta(x)=f(x-\theta)$. Let $K\subset\mathbb{R}$ be a compact set. I would like to compute (or at least lower bound) the following: $$ \inf_{\theta\ne\theta'\i …
2 votes
1 answer
69 views

Lower bounds on translates of a function

Let $f\in L^p(\mathbb{R})$ and define $f_\theta(x)=f(x-\theta)$. I would like to compute (or at least lower bound) the following: $$ \inf_{\theta\ne\theta'}\frac{\Vert f_\theta - f_{\theta'}\Vert_p}{| …