P. Agranovich, “Multi-term asymptotic representations of the Riesz measure of subharmonic functions in the plane”, Zh. Mat. Fiz. Anal. Geom., 2009, Volume 5, Number 1,Pages <nobr>3

Multi-term asymptotic representations of the Riesz measure of subharmonic functions in the plane

P. Agranovich

Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine

Abstract: In the paper, a multi-term asymptotic representation for distribution function of the Riesz measure of subharmonic function in the plane is considered. It is shown that the “smallness” of the reminder term of asymptotic representation does not guarantee the bounded variation with respect to the angle variable of all terms of this asymptotics, and the conditions for this property to be held are given.

Key words and phrases: Subharmonic function, the Riesz measure, multi-term asymptotic representation, function of bounded variation.

MSC: 31A05, 31A10, 26A45

Received: 02.08.2007

Language: English