Nguyen V. Problems of the theory of subharmonic and delta-subharmonic functions

The subject of investigation of the thesis includes entire, subharmonic, and delta-subharmonic functions in a finite-dimensional Euclidean space. The connection of convergence of sequences of delta-subharmonic functions in the sense of distributions with other kinds of convergence is studied as well as properties of Azarin's limit sets for delta-subharmonic functions and alternating Radon measures. Limit sets for wide class of delta-subharmonic functions and Radon measures are constructed; three criterions for a given set to be a limit set of some Radon measure are proved. The existence of an entire function of a given zero proximate order is proved.