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

Volume 200 / 2010

Alexander V. Abanin, Pham Trong Tien Studia Mathematica 200 (2010), 279-295 MSC: Primary 32A15; Secondary 32A17, 32A70, 32C99, 46E10. DOI: 10.4064/sm200-3-5

Abstract

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.

Authors

  • Alexander V. AbaninSouthern Institute of Mathematics
    Vladikavkaz 362027
    and
    Southern Federal University
    Rostov-na-Donu 344090
    The Russian Federation
    e-mail
  • Pham Trong TienSouthern Federal University
    Rostov-na-Donu 344090
    The Russian Federation
    e-mail

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