Let be a compactly supported, orthonormal scaling function that generates the linear space V0 2 L2(IR). We are motivated by the work of Walter and Shen [7]. In this paper, the authors use an Abel summation technique to build a positive scaling function Pr, 0 < r < 1, for the space V0. A reproducing kernel can in turn be constructed using Pr. This kernel is also positive, has unit integral, and ...

Aims: In this paper an approximate method for the solution of third-order differential equation with two and three point boundary condition is developed using iterative reproducing kernel method. Methods: The third order boundary value problem is converted into integro-differential equation of second order two point boundary value problem. The reproducing kernel method which takes the form of a...

We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). By applying method and representer theorem to perform linear quadratic in functional space, we derive recursive estimator dynamical system original input space. Unlike existing extensions Kalman where dynamics are assumed known, state-space representa...

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...