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

• Autorzy: Alexander V. Abanin , Pham Trong Tien
• Języki publikacji: EN

Abstrakty

EN

We prove a generalization of the well-known Hörmander theorem on continuation of holomorphic functions with growth conditions from complex planes in $ℂ^{p}$ into the whole $ℂ^{p}$. 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.

Kategorie tematyczne

• 32A17: Special families of functions
• 32A15: Entire functions
• 32A70: Functional analysis techniques \SeeMainly{}
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions
• 32C99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 200
• Numer: 3
• Strony: 279-295

Daty

wydano

2010

Twórcy

autor

Alexander V. Abanin

• Southern Institute of Mathematics, Vladikavkaz 362027
• Southern Federal University, Rostov-na-Donu 344090, The Russian Federation

autor

Pham Trong Tien

• Southern Federal University, Rostov-na-Donu 344090, The Russian Federation

Identyfikatory

DOI

10.4064/sm200-3-5