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When a genetic variant was found to be associated with established or advanced diabetic nephropathy (either at the allelic or genotypic level, including the recessive and dominant model) in two independent studies, that variant was considered to be a reproduced genetic variant.
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P is a reproducing cone in X. Proof.
Then P is a reproducing cone in X. Lemma 2.4 (Krein-Rutman) [8].
In the next theorem, we show that Ω is a reproducing kernel space, and we present its reproducing kernel.
At [9] prove that function space (W_2^1[a,b]) is a Hilbert space and also it is a reproducing kernel space.
Using Lemma 2.1, we prove that the functional space associated with inner norm is a reproducing kernel Hilbert space.
From [17, 18], W 2 1 [ 0, 1 ] is a reproducing kernel Hilbert space and the reproducing kernel is K 1 ( t, s ) = 1 + min { t, s } (2.2).
Ω is a reproducing kernel space, and its reproducing kernel is K_{n} x,y)=sum_{i=0}^{n}S_{i}(x S_{i} y).
Let be an interval and let be a reproducing kernel on.
Its Green function is a reproducing kernel for a suitable set of Hilbert space and an inner product.
If for any x ∈ X and x+, x- ∈ P, writing x = x+ + x- shows that P is a reproducing cone.
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