Noncritical holomorphic functions on Stein spaces

Holomorphic functions on Banach spaces

This is a survey about some problems from the theory of holomorphic functions on Banach spaces which have attracted the attention of many researchers during the last thirty years.

Holomorphic Submersions from Stein Manifolds

Holomorphic Submersions from Stein Manifolds

A special subspace of weighted spaces of holomorphic functions on the upper half plane

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

Compact Subsets of Spaces of Holomorphic Functions

In [1] compactness criteria in function spaces are investigated for general coorbit spaces. As an application it is shown that a bounded and closed subset A ⊂ F := {f : f is entire and Z C |f(z)|2e−|z| dλ(z) < ∞} is compact if and only if ∀2 > 0 ∃ a compact subset C ⊂ Cn with Z CC |f(z)|2e−|z| dλ(z) < 2 ∀f ∈ A. The methods of [1] cannot be easily adopted for the spaces Fm := {f : f is entire an...