Sets of uniqueness, weakly sufficient sets and sampling sets for weighted spaces of holomorphic functions in the unit ball

DOI10.1007/S11785-021-01144-0zbMath1478.32022arXiv1904.10634OpenAlexW3215826082MaRDI QIDQ2054451

Bingyang Hu, Le Hai Khoi

Publication date: 2 December 2021

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.10634

zbMATH Keywords

inductive limitsspaces of holomorphic functions in the ball

Mathematics Subject Classification ID

Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) (32A37)

Cites Work

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• Pre-dual of the function algebra \(A^{-\infty}(D)\) and representation of functions in Dirichlet series
• Hadamard gap series in weighted-type spaces on the unit ball
• Spaces with normal weights and Hadamard gap series
• Minimal absolutely representing systems of exponentials for \(A^{-\infty}(\varOmega)\)
• Weakly sufficient sets for \(A^{-\infty}(\mathbb D)\)
• Sampling sequences for \(A^{-\infty}\)
• Effective and sampling sets for Hörmander spaces
• Sampling sets and sufficient sets for \(A^{-\infty}\)
• WEAKLY SUFFICIENT SETS FOR WEIGHTED SPACES h_Φ^-∞(B)
• Dual of the function algebra 𝐴^{-∞}(𝐷) and representation of functions in Dirichlet series
• SETS OF UNIQUENESS, WEAKLY SUFFICIENT SETS AND SAMPLING SETS FOR A-∞(B)
• INDUCTIVE AND PROJECTIVE TOPOLOGIES. SUFFICIENT SETS AND REPRESENTING SYSTEMS
• Sampling sets for the space of holomorphic functions of polynomial growth in a ball
• Discrete Sufficient Sets for Some Spaces of Entire Functions
• Sufficient Sets for Some Spaces of Entire Functions

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