TY - JOUR

T1 - On some properties and examples of Nevanlinna domains

AU - Fedorovskii, K. Yu

N1 - Funding Information: This work was supported in part by the Russian Foundation for Basic Research (project no. 04-01-00720) and by the grant of the President of the Russian Federation for the support of leading scientific schools (project nos. NSh-2040.2003.1 and NSh-9429.2006.1).

PY - 2006/7

Y1 - 2006/7

N2 - The properties of Nevanlinna domains are considered. These domains arise in the problems of approximation by polyanalytic functions. Several analytic and geometric properties (both new and earlier known) of Nevanlinna domains are described. In particular, a new method for constructing Nevanlinna domains with boundaries belonging to the class C1 is proposed, and new examples of such domains whose boundaries do not belong to the class C1,α for α (0, 1) are presented. This method is based on the property of pseudocontinuation of a conformal mapping from the unit disk onto a Nevanlinna domain.

AB - The properties of Nevanlinna domains are considered. These domains arise in the problems of approximation by polyanalytic functions. Several analytic and geometric properties (both new and earlier known) of Nevanlinna domains are described. In particular, a new method for constructing Nevanlinna domains with boundaries belonging to the class C1 is proposed, and new examples of such domains whose boundaries do not belong to the class C1,α for α (0, 1) are presented. This method is based on the property of pseudocontinuation of a conformal mapping from the unit disk onto a Nevanlinna domain.

UR - http://www.scopus.com/inward/record.url?scp=33748317819&partnerID=8YFLogxK

U2 - 10.1134/S0081543806020155

DO - 10.1134/S0081543806020155

M3 - Article

AN - SCOPUS:33748317819

VL - 253

SP - 186

EP - 194

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -