What is it about?
The Nevanlinna class of meromorphic functions of bounded type, i.e. those representable as quotients of two bounded holomorphic functions, are of fundamental role in complex analysis. Such functions have have many good properties: existence of summable boundary values out of a zero-measure sets, a possibly simple representaion by those boundary values and zeros and poles of the function, etc. The article describes some subclasses of Nevanlinna's class in the half-plane, the functions of which have boundary values out of even zero-capacity sets.
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Why is it important?
The work gives a half-plane analog of M.M.Djrbashians exhaustive factorization theory of meromorphic functions, which is constructed by means of the mathematical apparatus of some analog of his general fractional integrodifferentiation.
Perspectives
Various problems of different mathematical features can be considered in relation with the classes of functions described in the article. Also, the technics of the M.M.Djrbashian general fractional integrodifferentiation and related representations can be applied for solving various problems.
Armen Jerbashian
University of Antioquia, Medellin, Colombia
Read the Original
This page is a summary of: A boundary property of some subclasses of functions of bounded type in the half-plane, Fractional Calculus and Applied Analysis, December 2017, De Gruyter,
DOI: 10.1515/fca-2017-0080.
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