Gleason's problem and homogeneous interpolation in hardy and dirichlet-type spaces of the ball

Daniel Alpay; H. Turgay Kaptanoǧlu

doi:10.1016/S0022-247X(02)00412-2

Gleason's problem and homogeneous interpolation in hardy and dirichlet-type spaces of the ball

Daniel Alpay, H. Turgay Kaptanoǧlu

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We solve Gleason's problem in the reproducing kernel Hilbert spaces with reproducing kernels 1/(1 - ∑ ₁ ^N z _j w̄ _j ) ^r for real r > 0 and their counterparts for r ≤ 0, and study the homogeneous interpolation problem in these spaces.

Original language	English
Pages (from-to)	654-672
Number of pages	19
Journal	Journal of Mathematical Analysis and Applications
Volume	276
Issue number	2
DOIs	https://doi.org/10.1016/S0022-247X(02)00412-2
State	Published - 15 Dec 2002
Externally published	Yes

Keywords

Dirichlet-type space
Gleason's problem
Homogeneous interpolation
Reproducing kernel Hilbert space
Schur multiplier
Shift and resolvent
Weighted Hardy space

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/S0022-247X(02)00412-2

Cite this

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title = "Gleason's problem and homogeneous interpolation in hardy and dirichlet-type spaces of the ball",

abstract = " We solve Gleason's problem in the reproducing kernel Hilbert spaces with reproducing kernels 1/(1 - ∑ 1 N z j {\=w} j ) r for real r > 0 and their counterparts for r ≤ 0, and study the homogeneous interpolation problem in these spaces.",

keywords = "Dirichlet-type space, Gleason's problem, Homogeneous interpolation, Reproducing kernel Hilbert space, Schur multiplier, Shift and resolvent, Weighted Hardy space",

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AU - Kaptanoǧlu, H. Turgay

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N2 - We solve Gleason's problem in the reproducing kernel Hilbert spaces with reproducing kernels 1/(1 - ∑ 1 N z j w̄ j ) r for real r > 0 and their counterparts for r ≤ 0, and study the homogeneous interpolation problem in these spaces.

AB - We solve Gleason's problem in the reproducing kernel Hilbert spaces with reproducing kernels 1/(1 - ∑ 1 N z j w̄ j ) r for real r > 0 and their counterparts for r ≤ 0, and study the homogeneous interpolation problem in these spaces.

KW - Dirichlet-type space

KW - Gleason's problem

KW - Homogeneous interpolation

KW - Reproducing kernel Hilbert space

KW - Schur multiplier

KW - Shift and resolvent

KW - Weighted Hardy space

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JF - Journal of Mathematical Analysis and Applications

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Gleason's problem and homogeneous interpolation in hardy and dirichlet-type spaces of the ball

Abstract

Keywords

ASJC Scopus subject areas

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