A Pointwise Bound for a Holomorphic Function which is Square-Integrable with Respect to an Exponential Density Function
| dc.creator | Chailuek, Kamthorn | |
| dc.creator | Lewkeeratiyutkul, Wicharn | |
| dc.date | 2003-12-17 | |
| dc.date.accessioned | 2026-07-07T05:04:01Z | |
| dc.date.available | 2026-07-07T05:04:01Z | |
| dc.description | 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 $z$. | |
| dc.description | 8 pages, no figure | |
| dc.identifier | https://arxiv.org/abs/math/0312341 | |
| dc.identifier | http://arxiv.org/abs/math/0312341 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69639 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.title | A Pointwise Bound for a Holomorphic Function which is Square-Integrable with Respect to an Exponential Density Function | |
| dc.type | text |