Article

Journal of Mathematical Sciences

, Volume 107, Issue 4, pp 4108-4124

Reproducing Kernels and Extremal Functions in Dirichlet-Type Spaces

  • S. M. ShimorinAffiliated withSt.Petersburg State University

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Abstract

Some identities are established for reproducing kernels and extremal functions in Dirichlet-type spaces. In certain cases, these identities are characteristic. A new proof of Aleman's theorem on extremal functions as contractive multipliers is obtained. In contrast to the original one, this proof can be extended to vector-valued spaces. Bibliography: 11 titles.