A Pointwise Bound for a Holomorphic Function which is Square-Integrable with Respect to an Exponential Density Function
Year: 2003
Type: preprint
Abstract: Let $ϕ$ be a real-valued smooth function on $\mathbf{C}$ satisfying $0 \le Δϕ\le M$ for some $M \ge 0$. We consider the space of all holomorphic functions which are square-integrable with respect to the measure $e^{-ϕ(z)} dz$. In this paper, a pointwise bound for any function in this space is established. We show that there exists a constant $K$ depending only on $M$ such that $|f(z)|^2 \le Ke^{ϕ(z)}\|f\|^2$ for any $f$ in this space and for any complex number $z$.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1554086129