Reproducing kernels for Hardy spaces on multiply connected domains

DOI10.1007/BF01192041zbMath0867.30038MaRDI QIDQ1921407

Kevin F. Clancey, Joseph A. Ball

Publication date: 4 August 1997

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

Hardy spacecurvaturetheta functionsreproducing kernelSchottky doublePick-Nevanlinna interpolation

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Spaces of bounded analytic functions of one complex variable (30H05) Linear operator methods in interpolation, moment and extension problems (47A57) Moment problems and interpolation problems in the complex plane (30E05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Spectral operators, decomposable operators, well-bounded operators, etc. (47B40) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (17)

The Use of Kernel Functions in Solving the Pick Interpolation Problem ⋮ The failure of rational dilation on a triply connected domain ⋮ Reflection positivity via Krein space analysis ⋮ Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued setting ⋮ Self-adjoint Toeplitz operators associated with representing measures on multiply connected planar regions and their eigenvalues ⋮ The trisecant identity and operator theory ⋮ Construction of Hardy spaces on Riemann surfaces with boundaries ⋮ Generalized interpolation in a multiply connected region ⋮ Indefinite Hardy spaces on finite bordered Riemann surfaces ⋮ Interpolation in semigroupoid algebras ⋮ Isometric representations of some quotients of \(H^\infty\) of an annulus ⋮ Eigenvalues of Toeplitz operators on the annulus and Neil algebra ⋮ Sources recovery from boundary data: A model related to electroencephalography ⋮ On the angles between subspaces, the Muckenhoupt condition, and projection from one co-invariant subspace onto another in the theory of character-automorphic Hardy spaces on a multiply connected domain ⋮ On the spectral character of Toeplitz operators on planar regions ⋮ Test functions in constrained interpolation ⋮ Analytic extensions and Cauchy-type inverse problems on annular domains: stability results

Cites Work

• The Pick interpolation theorem for finitely connected domains
• Representing measures on multiply connected planar domains
• A class of subnormal operators related to multiply-connected domains
• Operators of class \(C_{00}\) over multiply connected domains
• Theta functions on Riemann surfaces
• Extremal polynomials associated with a system of curves in the complex plane
• On the Szego Kernel of an Annulus
• The 𝐻^{𝑝} spaces of an annulus
• Complex geometry and operator theory
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