Journal of Mathematical Sciences

, Volume 107, Issue 4, pp 4108–4124

Reproducing Kernels and Extremal Functions in Dirichlet-Type Spaces


  • S. M. Shimorin
    • St.Petersburg State University

DOI: 10.1023/A:1012453003423

Cite this article as:
Shimorin, S.M. Journal of Mathematical Sciences (2001) 107: 4108. doi:10.1023/A:1012453003423


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.

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© Plenum Publishing Corporation 2001