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Suppose $f \colon I \to \mathbb{R}$ is a function in, say, $L^\infty$, and $I \subset \mathbb{R}$ is a bounded interval. We may assume further regularity on $f$, such as Lipschitz continuity or strict ...

Consider the Hilbert space $L^2_w$ with scalar product $\langle f,g\rangle_w =\int_0^\infty f(x)g(x)w(x)dx$ where the weight $w$ is the density function of a log-normal distribution $$ w(x)=\frac{1}{\...

Let $P(z)$ be a polynomial with complex variable $z$. We consider the following distribution for the roots of $P(z)=0$: the distribution is a triple $(n_{1},n_{2},n_{3})$ where these integers are ...