Strict superharmonicity of Mityuk’s function for countably connected domains of simple structure

Abstract

Strict superharmonicity of generalized reduced module as a function of a point (we call it Mityuk’s function) is established for the subclass of countably connected domains with unique limit point boundary component. The function just mentioned was first studied in detail by I.P. Mityuk and plays now an important role in the research of the exterior inverse boundary value problems of the theory of analytic functions in the multiply connected domains. At the heart of such a research one can see the fact that the critical points of Mityuk’s function are only maxima, saddles or semisaddles of corresponding surface. This fact is followed from the above strict superharmonicity.