Delta-subharmonic functions of completely regular gamma-growth in a half-plane

摘要

We consider entire, analytic, and delta-subharmonic functions of completely regular growth relative to the proximate order in a half-plane and to an arbitrary function of growth γ( r), which satisfies to the inequality γ(2r) ≤ Kγ( r) at some K > 0 and all r > 0. The concept of indicator h(θ,v) of a delta-subharmonic function v in a half-plane relative to γ( r)is introduced. It is proved that the indicator h(θ,v) belongs to the space L_2[0,π].