Gleason's problem and homogeneous interpolation in Hardy and Dirichlet-type spaces of the ball

DOI10.1016/S0022-247X(02)00412-2zbMath1022.47010MaRDI QIDQ1857004

H. Turgay Kaptanoğlu, Daniel Alpay

Publication date: 11 February 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Gleason's problemreproducing kernel Hilbert spaceDirichlet-type spacehomogeneous interpolation

Mathematics Subject Classification ID

Linear operator methods in interpolation, moment and extension problems (47A57) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs (32E30)

Related Items (12)

Canonical Transfer-function Realization for Schur-Agler-class Functions of the Polydisk ⋮ Aspects of multivariable operator theory on weighted symmetric Fock spaces ⋮ Reproducing kernels and radial differential operators for holomorphic and harmonic Besov spaces on unit balls: a unified view ⋮ Adaptative decomposition: the case of the Drury-Arveson space ⋮ Rational functions associated with the white noise space and related topics ⋮ Non-commutative Clark measures for the free and abelian Toeplitz algebras ⋮ Bergman inner functions and \(m\)-hypercontractions ⋮ Gleason's problem in infinite dimension ⋮ Projections for harmonic Bergman spaces and applications ⋮ Aleksandrov-Clark theory for Drury-Arveson space ⋮ Singularities of rational functions and minimal factorizations: the noncommutative and the commutative setting ⋮ Besov spaces and Bergman projections on the ball

Cites Work

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• Besov spaces and Bergman projections on the ball
• For which reproducing kernel Hilbert spaces is Pick's theorem true!
• Invariant subspaces and Nevanlinna-Pick kernels
• Automorphism invariant inner product in Hilbert spaces of holomorphic functions on the unit ball of \(\mathbb{C}^ n\)
• Integral formulas for a sub-Hardy Hilbert space on the ball with complete Nevanlinna–Pick reproducing kernel
• Sous-espaces de codimension finie dans la boule unité et un problème de factorisation
• Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem

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