Geodesic
On a Class of Analytic Functions of Smirnov
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 181-183

Voir la notice de l'article provenant de la source Cambridge University Press

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 . 
Schiff, J. L. On a Class of Analytic Functions of Smirnov. Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 181-183. doi: 10.4153/CJM-1979-018-3
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[1] 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] 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] 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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