On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions

Let I = ( a , b ) × ( c , d ) ⊂ R + 2 be an index set and let { G α ( x ) } α ∈ I be a collection of Gaussian functions, i.e. G α ( x ) = exp ( - α 1 x 1 2 - α 2 x 2 2 ) , where α = ( α 1 , α 2 ) ∈ I , x = ( x 1 , x 2 ) ∈ R 2 . We present a complete description of the uniformly discrete sets Λ ⊂ R 2...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2022-06, Vol.28 (3), Article 55
Main Author: Zlotnikov, Ilya
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Fourier Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Signal,Image and Speech Processing
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Summary:Let I = ( a , b ) × ( c , d ) ⊂ R + 2 be an index set and let { G α ( x ) } α ∈ I be a collection of Gaussian functions, i.e. G α ( x ) = exp ( - α 1 x 1 2 - α 2 x 2 2 ) , where α = ( α 1 , α 2 ) ∈ I , x = ( x 1 , x 2 ) ∈ R 2 . We present a complete description of the uniformly discrete sets Λ ⊂ R 2 such that every bandlimited signal f admits a stable reconstruction from the samples { f ∗ G α ( λ ) } λ ∈ Λ .
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-022-09948-0