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On Landau's Necessary Density Conditions for Sampling and Interpolation of Band‐Limited Functions
Author(s) -
Gröchenig K.,
Razafinjatovo H.
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/54.3.557
Subject(s) - citation , computer science , interpolation (computer graphics) , sampling (signal processing) , library science , mathematics , artificial intelligence , telecommunications , motion (physics) , detector
We give a new short proof of H. Landau's density result on necessary conditions for the sampling and interpolation of certain entire functions in the case that the boundary of the spectrum has measure 0. For the proof we adapt a method that has been recently developed by J. Ramanathan and T. Steger in the context of time‐frequency analysis. As a consequence of a general theorem for the comparison of densities we obtain several new results about the density of irregular sampling of band‐limited functions with derivatives and differential operators.