By Vladimir Ya. Eiderman, Mikhail V. Samokhin

This quantity is devoted to the reminiscence of the exceptional mathematician S.Ya. Khavinson. It starts with an expository paper via V.P. Havin proposing a finished survey of Khavinson's works in addition to sure biographical fabric. the total bibliography following this paper has now not formerly been released wherever. It includes 163 goods; a substantial a part of those can't be present in simply available assets. The ebook additionally features a sequence of pictures and twelve unique peer-reviewed learn and expository papers through top mathematicians world wide, together with the joint paper through S.Ya. Khavinson and T.S. Kuzina (the final book of S.Ya. Khavinson).

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52(94) (1960), 653–657. (Russian) [42] Approximation on sets of zero analytic capacity, Dokl. Akad. Nauk SSSR, 131 (1960), no. 1, 44–46. , Soviet Math. , 1 (1960), 205– 207. [43] On the radius of holomorphy of functions inverse to functions which are analytic and bounded in multiply connected regions, Izv. Vys. Uchebn. , Matematika, 1960, no. 5 (18), 190–194. (Russian) [44] Extremum problems for functions satisfying some supplementary restrictions inside the region and the application of these problems to questions of approximation, Dokl.

Royden [24] applied the duality method based on the Hahn-Banach theorem to study similar problems on finite Riemann surfaces not merely for bounded functions but also for general Hardy spaces functions. Ya. W. S. Shapiro [12]. ) Yet, the relevant study of dual extremal problems on finite Riemann surfaces, was limited to establishing “smooth” properties of the extremal functions near the boundary. Here, our goal is to describe the structure of extremal function in relation to the basic potential-theoretic functions on such surfaces: the Green and Neumann functions.

3, 379– 386. C. Tumarkin), Existence in multiply connected regions of single-valued analytic functions with a given modulus of boundary values, Izv. Akad. Nauk SSSR, Ser. , 22 (1958), no. 4, 543–562. C. Tumarkin), Conditions for the representability of a harmonic function by Green’s formula in a multiply connected region, Mat. , 44(86) (1958), no. 2, 225–234. C. Tumarkin), Properties of extremum functions in extremum problems for certain classes of analytic functions with a weighted metric, Dokl.

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