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Consider the following problem. Let $E,F,G$ be real or complex Banach spaces, such that $F\subset G$ with continuous embedding. Let $U\subset E$ an open set and $$ f:U\to G $$ an analytic map, such ...

$\def\zbar{\smash{\overline z}\vphantom z}$I would like to construct an approximation of the product \begin{equation} f(z) = \frac{1}{\zbar-a} \frac{1}{z-b}, \end{equation} where $a, b \in \mathbb{C}$,...

Let $a_1, a_2, \ldots : D\rightarrow\mathbb{R}$ be a sequence of continuous functions, with $D$ a compact metric space. Suppose that the function $f : D\times[0,\infty)\rightarrow\mathbb{R}$ given by $...

I'm curious whether lacunary functions (functions in the complex plane that are holomorphic in some open ball about the origin, but cannot be analytically extended past that ball) are typical or the ...