A Pointwise Bound for a Holomorphic Function which is Square-Integrable with Respect to an Exponential Density Function
Chailuek, Kamthorn ; Lewkeeratiyutkul, Wicharn
arXiv, 0312341 / Harvested from arXiv
Text on arXiv
Let $\phi$ be a real-valued smooth function on $\mathbf{C}$ satisfying $0 \le \Delta \phi \le M$ for some $M \ge 0$. We consider the space of all holomorphic functions which are square-integrable with respect to the measure $e^{-\phi(z)} dz$. 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 $|f(z)|^2 \le Ke^{\phi(z)}\|f\|^2$ for any $f$ in this space and for any complex number $z$.
Publié le : 2003-12-17
Classification:  Mathematics - Functional Analysis,  Mathematical Physics 
@article{0312341,
     author = {Chailuek, Kamthorn and Lewkeeratiyutkul, Wicharn},
     title = {A Pointwise Bound for a Holomorphic Function which is Square-Integrable
  with Respect to an Exponential Density Function},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312341}
}

Chailuek, Kamthorn; Lewkeeratiyutkul, Wicharn. A Pointwise Bound for a Holomorphic Function which is Square-Integrable
  with Respect to an Exponential Density Function. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312341/