Real-analytic continuation along a fixed direction. (English) Zbl 1522.32023
Summary: 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 \((dd^cu)^n.\)
Keywords:
real-analytic functions; separately-analytic functions; Green function; homogeneous power series; \( \mathcal{P} \)-measureReferences:
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