Single-point extremal functions in weighted bergman spaces

For weighted Berman spaces in the unit disk the extremal functions for invariant subspaces formed by functions vanishing at a fixed point are studied. In the case where the weight is radial and logarithmically subharmonic, it is shown that such extremal functions can serve for the separation of single zeros. It is also proved that the reproducing kernels of the Bergman spaces are univalent functions. Bibliography: 7 titles. Translated fromProblemy Matematicheskogo Analiza, No. 15, 1995, pp. 241–252.