Hi , what is Gaussian kernel and its width parameter? How should I choose the width parameter ?

I am trying to understand a proof by G.Wagner in his paper "On Means on Distances on the Surface of a Sphere (Lower Bounds)": http://projecteuclid.org/DPubS/Repository/1.0/Dissemin …

Let $H$ be a Reproducing Kernel Hilbert Space with elements $f:X\rightarrow \mathbb{C}$, with kernel $K(x, y)$. My question is whether, for some choice of $x_i\in X$, it is the cas …

Consider the following exponential kernel: $k(x_1, x_2) = \exp\left(\frac{|x_1 - x_2|}{L}\right)$, which is symmetric and non-negative definite. By virtue of Mercer's theorem, we …

Hello, I know that $k(x,y)=min(x,y)$ is the reproducing kernel of the Cameron Martin space of all i.i.d. RVs of Brownian motion at different times, with the $cov$ inner product. …

Hi, I need an estimation or an exact closed form expression for the following integral $\int_{0}^{2\pi} K_N^4(s) ds $ where $K_N(s)= \frac{1}{N2\pi} (\frac{sin(Ns/2)}{sin(s/2)}) …

Let $K(x,y): \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ given by $K(x,y) = e^{-< x,y>^2}$ where $<\cdot,\cdot>$ denote the canonical inner product. Define integral oper …

I was wondering if it possible to find a measure $\eta$ on $\mathbb{R}$ such that $$ L(x):=\log\frac{1}{|x|}=\int e^{itx}\;d\eta(t) $$ for every $x\in [0,1/2]$. On a structural …

I'm a CS student and I'm trying to learn RKHS theory to understand the passages made in this paper . Among the bibliography I'm using there are "On the mathematical fundamentals of …

Let $M$ be a $n-$dim real smooth manifold and let $\alpha \in \Omega^{2}(M)$. How is the kernel bundle $ker(\alpha)$ defined ? Do we need some other assumptions on the form $\alpha …

Hi, I am doing some Kernel density estimation, with a weighted points set (ie., each sample has a weight which is not necessary one), in N dimensions. Also, these samples are just …