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Does there exist a function which is holomorphic in $|z|<1,$ continuous in $|z|\leq1$ and such that the series $\sum |a_n|$ is divergent, where $a_n$'s coefficients in the Taylor series expansion ...

Let $$h : \mathbb{R}^2 \to \mathbb{R}^+.$$ Suppose that for each $x$, $h(x, y)$ is a real analytic function of $y$. Let $\mu(dx)$ be a finite measure on $\mathbb{R}$, and for each $y$, suppose that $$...

Hi all. I want to construct a power series $F(z)=\sum_{n=0}^\infty c_nz^n$ centered at zero and with finite radius of convergence in the complex plane, and which has infinitely many zeros (in its ...