Sufficient conditions are established in order that, for a fixed infinite set of sampling points on the full line, a function satisfies a sampling theorem on a suitable closed subspace of a unitarily translation invariant reproducing kernel Hilbert space. A number of examples of such reproducing kernel Hilbert spaces and the corresponding sampling expansions are given. Sampling theorems for fun...

We propose a fully Bayesian methodology for generalized kernel mixed models (GKMMs), which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of a generalized kernel model (GKM). This mixture prior allows a fraction of the components of the regres...

In order to use the method of(least squares) collocation for the computation o f an approximation to the anomalous potential o f the Earth (T) it is necessary to specify a reproducing kernel Hilbert space the dual o.f which contain the (linear) functionals associated with the observation~ The specification includes the prescription o f an inner product or an equivalent norrrL It is demonstrated...

Given a positive definite, bounded linear operator A on the Hilbert space H0 := l(E), we consider a reproducing kernel Hilbert space H+ with a reproducing kernel A(x, y). Here E is any countable set and A(x, y), x, y ∈ E, is the representation of A w.r.t. the usual basis of H0. Imposing further conditions on the operator A, we also consider another reproducing kernel Hilbert space H − with a ke...

We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the wei...

In this study, the numerical solution of Fredholm integro–differential equation is discussed in a reproducing kernel Hilbert space. A reproducing kernel Hilbert space is constructed, in which the initial condition of the problem is satisfied. The exact solution u x ð Þ is represented in the form of series in the space W 2 2 ½a; bŠ. In the mean time, the n-term approxima te solution u n ðxÞ is o...

The problem of finding the pattern that deviates from other observation is termed as outlier. detection outlier getting importance in research area nowadays due to reason technique has been used various mission critical applications such military, health care, fault recovery, and many. analysis functional data its depth function plays a crucial role statistical model for detecting values alone ...