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On a Class of Analytic Functions of Smirnov
Published online by Cambridge University Press: 20 November 2018
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The class S of functions under study in this paper was introduced by V. I. Smirnov in 1932. This class was subsequently investigated by various authors, a pertinent paper to the present wrork being that of Tumarkin and Havinson [2], who showed that a plane compact set of logarithmic capacity zero is 5-removable. Another important development, due to Yamashita [3], wras that the class 5 could be characterized as those analytic functions ƒ for which log+ |ƒ| has a quasi-bounded harmonic majorant.
In what follows, we discuss the Smirnov class in the context of planar surfaces, exploiting some ideas in the work of Hejhal [1] to establish that a closed, bounded, totally disconnected set is S-removable if and only if its complement belongs to the null class Os.
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- Research Article
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- Copyright © Canadian Mathematical Society 1979
References
1.
Hejhal, D. A., Classification theory for Hardy classes of analytic functions, Ann. Acad. Sci. Fenn. Ser. A. (1974), p. 1–29.Google Scholar
2.
Tumarkin, G. Ts. and Havinson, S. Ya., On removal of singularities of analytic functions of a class (class D), Uspehi Matem. Nau. 12 (1957), 193–199. (Russian).Google Scholar
3.
Yamashita, S., On some families of analytic functions on Riemann surfaces, Nagoya Math. J. 31 (1968), 57–68.Google Scholar
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