Continuation of holomorphic functions with growth conditions and some of its applications
Tom 200 / 2010
Studia Mathematica 200 (2010), 279-295
MSC: Primary 32A15; Secondary 32A17, 32A70, 32C99, 46E10.
DOI: 10.4064/sm200-3-5
Streszczenie
We prove a generalization of the well-known Hörmander theorem on continuation of holomorphic functions with growth conditions from complex planes in ${\mathbb C}^p$ into the whole ${\mathbb C}^p$. We apply this result to construct special families of entire functions playing an important role in convolution equations, interpolation and extension of infinitely differentiable functions from closed sets. These families, in their turn, are used to study optimal or canonical, in a certain sense, weight sequences defining inductive and projective type spaces of entire functions with $O$-growth conditions. Finally, we give a natural and complete description of multipliers for spaces given by canonical weight sequences.
