Variation of Subharmonic Function under Transformation of its Riesz Measure

Abstract

The paper combines two aspects. First, it contains a compressed com- parative review of the well-known results on the change of growth of entire (subharmonic resp.) function under the shifts of its zeros (under T-shift of its Riesz measure resp.). There was B.Ya. Levin who stood at the sources of these results. Second, the rst coauthor proves new results obtained in this direction: the estimates of change of subharmonic function under integral restrictions for T-shift of its Riesz measure, and also, in a certain sense, an optimal approximation of an entire function by the entire function with simple zeros.