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- Title
Perturbation Theorems for Regular Sampling in Wavelet Subspaces.
- Authors
Antony Selvan, A.; Priyanka, Kumari
- Abstract
A perturbation theorem for regular sampling in the Paley-Wiener space, also known as the Kadec 1 / 4 -theorem, states that if { x k : k ∈ Z } is a sequence of real numbers for which L = sup k ∈ Z | x k − k | < 1 / 4 , then any entire function f ∈ L 2 (R) of exponential type at most π can be recovered from its samples { f (x k) : k ∈ Z } . Kadec-type theorems for irregular sampling in wavelet subspaces have been discussed in several papers. However, the optimal value of L is found only in the Franklin spline wavelet subspace. This paper aims to find a better bound for L in the Kadec-type theorem for wavelet subspaces along with sampling bounds.
- Subjects
SAMPLING theorem; INTEGRAL functions; REAL numbers; IRREGULAR sampling (Signal processing); SPLINE theory
- Publication
Acta Applicandae Mathematicae, 2022, Vol 182, Issue 1, p1
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-022-00542-6