Möbius Instability of Sampling for Small Weighted Spaces of Analytic Functions | Zendy

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Möbius Instability of Sampling for Small Weighted Spaces of Analytic Functions

Author(s) -

Dhuez Rémi

Publication year - 2005

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609305004790

Subject(s) - mathematics , holomorphic function , space (punctuation) , instability , mathematics subject classification , sampling (signal processing) , pure mathematics , unit disk , stability (learning theory) , mathematical analysis , philosophy , linguistics , physics , filter (signal processing) , machine learning , computer science , mechanics , computer vision

In this paper, the space A ψ (D)is considered, consisting of those holomorphic functions f on the unit disk D such that ‖ f ‖ ψ = sup z ∈ D | f ( z )|ψ(| z |) < +∞, with ψ(1) = 0. The sampling problem is studied for weights satisfying ln ψ( r )/ln(1 − r ) → 0. Möbius stability of sampling is shown to fail in this space. 2000 Mathematics Subject Classification 30H05 (primary), 30D60 (secondary).

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