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BY 4.0 license Open Access Published by De Gruyter Open Access December 13, 2019

Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

  • Andriy Bandura EMAIL logo , Oleh Skaskiv and Liana Smolovyk
From the journal Demonstratio Mathematica

Abstract

In the paper we investigate slice holomorphic functions F : ℂn → ℂ having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 + tb : t ∈} for an arbitrary z0 n and for the fixed direction b ∈ℂn \ {0}, and (∃m0 ∈ ℤ+) (∀m ∈ +) (∀z ∈ n) the following inequality holds

|bmF(z)|m!Lm(z)max0km0|bkF(z)|k!Lk(z),

where L : ℂn+ is a positive continuous function, bF(z)=ddtF(z+tb)|t=0,bpF=b(bp-1F)for p ≥ 2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differential equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

MSC 2010: 32A10; 32A17; 32A37; 30H99; 30A05

References

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Received: 2019-07-27
Accepted: 2019-11-03
Published Online: 2019-12-13

© 2019 Andriy Bandura et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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