Entire Functions

Abstract

We consider the basic problems, notions and facts in the theory of entire functions of several variables, i.e. functions f (z) holomorphic in the entire space ℂn (i.e. f∈H(ℂn). Such functions constitute an independent object of study and are often encountered in applications of complex analysis to other branches of mathematics. For instance, entire functions of several variables are widely used in the theory of linear p.d.e. [8], [32], in the theory of convolution equations [31], in the theory of distributions [12], [51], in probability theory [26]. There are also numerous applications of entire functions of several variables in various branches of physics.KeywordsHolomorphic FunctionEntire FunctionAlgebraic VarietyFinite TypeInterpolation ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.