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autora: Alexander V. Abanin

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

100%

Abanin A., Tien P.

Studia Mathematica

2010

tom 200

nr 3

279-295

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.

Erratum to: "Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces" (Studia Math. 213 (2012), 169-187)

100%

Abanin A., Tien P.

Studia Mathematica

2013

tom 215

nr 3

287-289

Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces

100%

Abanin A., Tien P.

Studia Mathematica

2012

tom 213

nr 2

169-187

We obtain, in terms of associated weights, natural criteria for compact embedding of weighted Banach spaces of holomorphic functions on a wide class of domains in the complex plane. Our study is based on a complete characterization of finite-dimensional weighted spaces and canonical weights for them. In particular, we show that for a domain whose complement is not a Painlevé null set each nontrivial space of holomorphic functions with O-growth condition is infinite-dimensional.

Ograniczanie wyników

3 Studia Mathematica

3 Abanin A.

3 Tien P.

1 2013

1 2012

1 2010

Wyniki wyszukiwania

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

Erratum to: "Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces" (Studia Math. 213 (2012), 169-187)

Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces