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A note on the Nullstellensatz for c-holomorphic functions

Maciej P. Denkowski (2007)

Annales Polonici Mathematici

We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection, generalizing...

Invariant Functions on Neil Parabola in Cn

Zapalowski, Pawel (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 32F45.We present the Carathéodory and the inner Caratheodory distances and the Carathéodory-Reiffen metric on generalized Neil parabolas in Cn. It is a generalization of the results from [4] and [5].This work is a part of the Research Grant No. 1 PO3A 005 28, which is supported by public means in the programme promoting science in Poland in the years 2005–2008.

Maximum modulus in a bidisc of analytic functions of bounded 𝐋 -index and an analogue of Hayman’s theorem

Andriy Bandura, Nataliia Petrechko, Oleh Skaskiv (2018)

Mathematica Bohemica

We generalize some criteria of boundedness of 𝐋 -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of ( p + 1 ) th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).

On Some of Professor Peter Rusev's Contributions

Kiryakova, Virginia (2012)

Mathematica Balkanica New Series

MSC 2010: 33-00, 33C45, 33C52, 30C15, 30D20, 32A17, 32H02, 44A05The 6th International Conference "Transform Methods and Special Functions' 2011", 20 - 23 October 2011 was dedicated to the 80th anniversary of Professor Peter Rusev, as one of the founders of this series of international meetings in Bulgaria, since 1994. It is a pleasure to congratulate the Jubiliar on behalf of the Local Organizing Committee and International Steering Committee, and to present shortly some of his life achievements...

Tautness of locally taut domains in complex spaces

Do Duc Thai, Pham Nguyen Thu Trang (2004)

Annales Polonici Mathematici

A necessary and sufficient condition for tautness of locally taut domains in a weakly Brody hyperbolic complex space is given. Moreover, some results of Kobayashi and Gaussier are deduced as corollaries.

The Łojasiewicz exponent of c-holomorphic mappings

Maciej P. Denkowski (2005)

Annales Polonici Mathematici

The aim of this paper is to study the Łojasiewicz exponent of c-holomorphic mappings. After introducing an order of flatness for c-holomorphic mappings we give an estimate of the Łojasiewicz exponent in the case of isolated zero, which is a generalization of the one given by Płoski and earlier by Chądzyński for two variables.

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