Extremal functions in invariant subspaces of Bergman spaces

zbMath0853.30023MaRDI QIDQ1922054

Peter Duren, Harold S. Shapiro, Dmitry Khavinson

Publication date: 11 December 1996

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Bergman spacesanalytic continuationinner functionextremal functioncanonical divisor

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Banach spaces of continuous, differentiable or analytic functions (46E15) Entire and meromorphic functions of one complex variable, and related topics (30D99)

Related Items (17)

On the geometry of the multiplier space of \(\ell^p_A\) ⋮ Vanishing Bergman kernels on the disk ⋮ The Green function for the weighted biharmonic operator \(\Delta(1-| z|^2)^{-\alpha}\Delta\), and factorization of analytic functions ⋮ Maximal Blaschke products ⋮ Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants ⋮ Analogues of finite Blaschke products as inner functions ⋮ Finite unions of interpolation sequences ⋮ Solution of extremal problems in Bergman spaces using the Bergman projection ⋮ The majorization function and the index of invariant subspaces in the Bergman spaces. ⋮ The zero sets of \(\ell^p_A\) are nested ⋮ Inner functions and zero sets for ℓ^{𝑝}_{𝐴} ⋮ A Blaschke sequence that is not a zero set for ℓ^{𝑝}_{𝐴} ⋮ On the failure of canonical factorization in \(\ell_A^p\) ⋮ Mean value surfaces with prescribed curvature form ⋮ A sharp estimate for extremal functions ⋮ Critical Points, the Gauss Curvature Equation and Blaschke Products ⋮ Multiple interpolation and extremal functions in the Bergman spaces.

This page was built for publication: Extremal functions in invariant subspaces of Bergman spaces