# Tagged Questions

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### A Fourier analysis-type identity arising in potential theory

I have recently been learning about potential theory in the complex plane, and I would like to understand why the following proposition is true:
Suppose $f: \mathbb C \to \mathbb R$ is smooth, ...

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### On a limit at the boundary of $\mathbb{D}$ related to complex and harmonic analysis

Let $p(z,t)=\frac{1}{2\pi}.\frac{1-|z|^2}{|z-t|^2}$ be the Poisson kernel on the open unit disk $\mathbb{D}$, fix $0<\alpha<1$ . Let $a\in \partial\mathbb{D}=S^1$ be fixed. Then my question is :
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186 views

### A variational problem involving a negative fractional Soboblev norm.

I've run into the problem of trying to evaluate the following:
$\max_{ \xi} \iint_{\partial B \times \partial B} \xi(x) \Phi(|x-y|) \xi(y) dS(x)dS(y)$
subject to $\int_{\partial B} \xi(y)dS(y) = 0$ ...