RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Ufimsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 Ufimsk. Mat. Zh., 2011, Volume 3, Issue 4, Pages 86–94 (Mi ufa120)

The indicator of a delta-subharmonic function in a half-plane

a Sumy State University, Sumy, Ukraine
b Istanbul University, Fen Fakultesi, Matematik Bolumu, Istanbul, Turkey

Abstract: Delta-subharmonic functions of a completely regular growth in the upper half-plane have been introduced in the joint work of the authors, published in Reports of the Russian Academy of Sciences (2001). In this work, criteria whether a delta-subharmonic function in the upper half-plane belongs to a class of functions of a completely regular growth have been obtained on the basis of the theory of Fourier coefficients of delta-subharmonic functions in the half-plane developed in the beginning of this century by the first author of the present article. The present paper is a natural continuation of this research. The concept of the indicator of a delta-subharmonic function of a completely regular growth in the upper half-plane is introduced. It is proved that the indicator of a delta-subharmonic function of a completely regular growth in the upper half-plane belongs to a class $L_p[0,\pi]$ ($1<p\leq2$). The proof is based on the lemma about Polya peaks and the Hausdorff–Young theorem.

Keywords: delta-subharmonic functions of a completely regular growth in the upper half-plane, Fourier coefficients, the indicator, Polya peaks, Hausdorff–Young theorem.

Full text: PDF file (430 kB)
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
UDC: 517.9

Citation: K. G. Malyutin, N. Sadik, “The indicator of a delta-subharmonic function in a half-plane”, Ufimsk. Mat. Zh., 3:4 (2011), 86–94

Citation in format AMSBIB
\Bibitem{MalSad11} \by K.~G.~Malyutin, N.~Sadik \paper The indicator of a~delta-subharmonic function in a~half-plane \jour Ufimsk. Mat. Zh. \yr 2011 \vol 3 \issue 4 \pages 86--94 \mathnet{http://mi.mathnet.ru/ufa120} \zmath{https://zbmath.org/?q=an:1249.30096}