Positive-Definiteness and its Applications to Interpolation Problems for Holomorphic Functions

DOI10.2307/1999286zbMath0574.32024OpenAlexW4234403348MaRDI QIDQ3693823

Jacob Burbea, Frank jun. Beatrous

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999286

zbMATH Keywords

unicityextension of holomorphic functionspositive kernelHilbert spaces of holomorphic functionsinterpolating bounded holomorphic functions

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs (32E30) Algebras of holomorphic functions of several complex variables (32A38)

Related Items (19)

Interpolation for multipliers on reproducing kernel Hilbert spaces ⋮ de Branges–Rovnyak Spaces: Basics and Theory ⋮ de Branges–Rovnyak Spaces and Norm-Constrained Interpolation ⋮ Kernel decompositions for Schur functions on the polydisk ⋮ Weighted sub-Bergman Hilbert spaces in the unit ball of \(\mathbb{C}^n\) ⋮ Positive extension problems for a class of structured matrices. ⋮ Pick-Nevanlinna interpolation theorem and multiplication operators on functional Hilbert spaces ⋮ Reproducing Properties of Holomorphic Kernels on Balls of ℂ^q ⋮ Abstract interpolation in vector-valued de Branges-Rovnyak spaces ⋮ Inequalities for weighted \(L^ 2\)-functions on the half-line ⋮ Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem ⋮ Sub-Bergman spaces in the unit ball of ℂⁿ ⋮ For which reproducing kernel Hilbert spaces is Pick's theorem true! ⋮ Interpolation in de Branges-Rovnyak spaces ⋮ Mathematical work of Franciszek Hugon Szafraniec and its impacts ⋮ On an intertwining lifting theorem for certain reproducing kernel Hilbert spaces ⋮ On bounded holomorphic interpolation in several variables ⋮ Interpolation in Sub-Bergman Spaces ⋮ A lifting theorem for subordinated invariant kernels

Cites Work

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• \(H^\infty\) interpolation from a subset of the boundary
• Lower order positivity and holomorphic operators
• Reproducing kernel spaces and analytic continuation
• Operator-valued Pick's conditions and holomorphicity
• Pick's theorem with operator-valued holomorphic functions
• The Cauchy and the Szegoe kernels on multiply connected regions
• Restrictions of \(H^p\) functions to the diagonal of the polydisc
• Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Berman spaces
• Quadratic inequalities and analytic continuation
• On Quadratic and Bilinear Forms in Function Theory
• Inequalities for Holomorphic Functions of Several Complex Variables
• On Differentiability at the Boundary in Conformal Mapping
• Holomorphic Functions With Positive Real Part on Polycylinders
• Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)
• Theory of Reproducing Kernels

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