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Studia Mathematica

2010 | 200 | 3 | 279-295

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

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.

279-295

wydano
2010

Twórcy

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