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In this paper, we discuss the explicit solution of certain extremal problems in Bergman spaces. In order to do this, we develop methods to calculate the Bergman projections of various functions. As a special case, we deal with canonical divisors for certain values of
Using Zalcman’s lemma, we study a uniqueness question of meromorphic functions, where the meromorphic functions and their certain non-linear differential polynomials share a non-zero value with their shifts. The results in this paper extends Theorem 1 in Yang and Hua (Ann Acad Sci Fenn Math...
is a holomorphic function in the unit disk. We provide bounds for the distance of
from its linearization
; the bounds involve the area, the diameter or the logarithmic capacity of the image...
In this paper, we construct an explicit parameterisation describing quadrature domains of finite area and arbitrary finite connectivity admitting quadrature identities with integrals along interior arcs. The formulation is in terms of conformal maps from circular domains, where these maps are...
denote the set of all polynomials with positive integer coefficients which have their zeros in the open left half-plane. We are looking for polynomials in
whose largest coefficients are as small as possible and also for polynomials in...
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