Real-Analytic Continuation Along a Fixed Direction

The paper is devoted to studying analytic continuations of functions of several variables that are $${\mathbb{R}}$$ -analytic along a fixed direction. The presented results have direct relation with the well-known Hartogs theorem on the analyticity of separately-analytic functions in multidimensional complex analysis. However, their studies is significantly different. In this work, the main method for studying continuations of $${\mathbb{R}}$$ -analytic functions is based on the use of the rich properties of analytic functions of several variables and the pluripotential theory based on the Monge–Ampere operator $$(dd^{c}u)^{n}.$$