Optimal sampling points in reproducing kernel Hilbert spaces
نویسندگان
چکیده
منابع مشابه
Optimal Sampling Points in Reproducing Kernel Hilbert Spaces
The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We are motivated to study the optimal distribution of finite sampling points. Formulation under the framework of optimal reconstruction yields a minimization pro...
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We investigate the construction of all reproducing kernel Hilbert spaces of functions on a domain Ω ⊂ R that have a countable sampling set Λ ⊂ Ω. We also characterize all the reproducing kernel Hilbert spaces that have a prescribed sampling set. Similar problems are considered for reproducing kernel Banach spaces, but now with respect to Λ as a p-sampling set. Unlike the general p-frames, we pr...
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P (α) = C(α, F (x, y)) = αF (x, x) + 2αF (x, y) + F (x, y)F (y, y), which is ≥ 0. In the case F (x, x) = 0, the fact that P ≥ 0 implies that F (x, y) = 0. In the case F (x, y) 6= 0, P (α) is a quadratic polynomial and because P ≥ 0 it follows that the discriminant of P is ≤ 0: 4F (x, y) − 4 · F (x, x) · F (x, y)F (y, y) ≤ 0. That is, F (x, y) ≤ F (x, y)F (x, x)F (y, y), and this implies that F ...
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An account of sampling in the setting of reproducing kernel spaces is given, the main point of which is to show that the sampling theory of Kluvánek, even though it is very general in some respects, is nevertheless a special case of the reproducing kernel theory. A Dictionary is provided as a handy summary of the essential steps. Starting with the classical formulation, the notion of band-limit...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2016
ISSN: 0885-064X
DOI: 10.1016/j.jco.2015.11.010