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

6 votes
Accepted

Can I find a bump function $\psi$ such that $\nabla\log\psi$ vanishes too?

Elaborating the comment by Wojowu: If we take a look at $n=1$ and $\psi\in C^\infty_{\text c}(\mathbb R)$ is a function satisfying conditions 1., 2. and 3. of your question, then for every $x\in]-1,1[ …
Maximilian Janisch's user avatar
3 votes
0 answers
450 views

Opposite of the curl operator and Biot-Savart kernel

Note: I just realized that using $\omega$ and $w$ might not have been the smartest choice of notation -- Sorry about that. Let $\renewcommand{\div}{\operatorname{\div}}Q_0, Q_1$ be two real numbers, $ …