Abstract
Let G be a finitely-connected plane domain with analytic boundary Г denote by A the area of G, and by P its perimeter. The analytic content λ of G is the uniform distance from the function [zbar] to the uniform algebra A(G) of functions holomorphic inside G which are continuous up to Г. D. Khavinson has conjectured that λ = 2A/P if, and only if, G is a disk or an annulus. In an attempt to settle down this conjecture we reformulate it in terms of potential theory and of quadrature identities for certain classes of harmonic and holomorphic functions. Some characterizations of disks and annuli along those lines are obtained. AMS No. 30E10, 31A25, 30E20
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