2013
DOI: 10.1007/s10440-013-9860-1
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The Kramer Sampling Theorem Revisited

Abstract: The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide, in an unified way, new and old generalizations of this result corresponding to various different settings; all these generalizations are illustrated with examples. All the different situations along the paper share a basic … Show more

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Cited by 9 publications
(9 citation statements)
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“…After some straightforward calculations (see [9,12] for the details), any f ∈ V 2 ϕ can be expressed as…”
Section: Some Preliminaries On Shift-invariant Subspacesmentioning
confidence: 99%
See 3 more Smart Citations
“…After some straightforward calculations (see [9,12] for the details), any f ∈ V 2 ϕ can be expressed as…”
Section: Some Preliminaries On Shift-invariant Subspacesmentioning
confidence: 99%
“…Thus, convergence in the L 2 (R)-norm implies pointwise convergence which is uniform on R since the function t → K t 2 = n∈Z |ϕ(t − n)| 2 is assumed to be bounded on R. As a consequence, from now on we are only concerned with L 2 (R)-norm convergence. See more details in [12,13].…”
Section: Some Preliminaries On Shift-invariant Subspacesmentioning
confidence: 99%
See 2 more Smart Citations
“…Since then, various RKBSs [13,16,38,39,44,47,48,50] have been constructed for different applied and theoretical purposes. They are used in a wide variety of fields such as machine learning [44,47,48,50,51], sampling reconstruction [14,15,18,27,28], sparse approximation [38,39,44,47], and functional analysis [9,36,49]. The definitions of existing RKBSs and the associated reproducing kernels in the literature are dependent on the construction.…”
Section: Introductionmentioning
confidence: 99%