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On Reproducing Kernel Hilbert Spaces of Polynomials
Mathematische Nachrichten, 1997AbstractCertain Hilbert spaces of polynomials, called Szegö spaces [11], are studied. A transformation, called Hilbert traneformation, is constructed for every polynomial associatted with a Szegö space. An orthogonal set is found in a Szegö space which determines the norm of the space. A matrix factorization theory is obtained for defining polynomials.
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Pasting Reproducing Kernel Hilbert Spaces
2017The aim of this article is to find the necessary and sufficient condition for the mapping $$\displaystyle{H_{K}(E) \ni f\mapsto (\,f\vert E_{1},f\vert E_{2}) \in H_{K\vert E_{1}\times E_{2}}(E_{1}) \oplus H_{K\vert E_{2}\times E_{2}}(E_{2})}$$ to be isomorphic, where K is a positive definite function on E = E1 + E2.
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Reproducing Kernel Hilbert Spaces and Discrimination
2015In this chapter, it is examined to what extent RKHS’s allow one to discriminate between probability laws, that is determine their equivalence or singularity.
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
exaly
Sampling in Reproducing Kernel Hilbert Space
2014An 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 Kluvanek, 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.
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
exaly
Rainfall-runoff modeling through regression in the reproducing kernel Hilbert space algorithm
Journal of Hydrology, 2020M. Safari +2 more
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Relations Between Reproducing Kernel Hilbert Spaces
2015When one claims that the signal must be in the RKHS of the noise, for detection to be nonsingular, one in fact means that the family of its paths should be contained, as a set, in the RKHS of that noise. One shall see in the next chapter that such a requirement entails a specific inclusion of related RKHS’s, and the entire topic may be seen as a ...
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