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On the distribution of values of generalized analytic functions. (English. Russian original) Zbl 0658.30043
Sov. Math., Dokl. 36, No. 2, 379-381 (1988); translation from Dokl. Akad. Nauk SSSR 269, 1293-1296 (1987).
A function f in the big-plane \(\Omega\) over a compact group with ordered dual is said to be meromorphic in \(\Omega\) if it is analytic (in the sense of Arens-Singer) on the whole of \(\Omega\) with the possible exception of a “thin” subset E of \(\Omega\) and if the set of essential singularities of f is nowhere dense in E. The author has introduced the notions of measures of the sets of zeros and poles of meromorphic functions in the big-plane and has found some important relations between them, analogical to the classical ones.
Reviewer: T.Tonev
30G30 Other generalizations of analytic functions (including abstract-valued functions)
30G35 Functions of hypercomplex variables and generalized variables
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory