Continuation of holomorphic functions with growth conditions and some of its applications

Alexander V. Abanin ¹   ; Pham Trong Tien ²

¹ Southern Institute of Mathematics Vladikavkaz 362027 and Southern Federal University Rostov-na-Donu 344090 The Russian Federation
² Southern Federal University Rostov-na-Donu 344090 The Russian Federation

Studia Mathematica, Tome 200 (2010) no. 3, pp. 279-295

Résumé

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.

Détail

DOI : 10.4064/sm200-3-5

Keywords: prove generalization well known rmander theorem continuation holomorphic functions growth conditions complex planes mathbb whole mathbb apply result construct special families entire functions playing important role convolution equations interpolation extension infinitely differentiable functions closed sets these families their turn study optimal canonical certain sense weight sequences defining inductive projective type spaces entire functions o growth conditions finally natural complete description multipliers spaces given canonical weight sequences