Ognyan Kounchev

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We study the existence and shape preserving properties of a generalized Bernstein operator Bn fixing a strictly positive function f0, and a second function f1 such that f1/f0 is strictly increasing, within the framework of extended Chebyshev spaces Un. The first main result gives an inductive criterion for existence: suppose there exists a Bernstein(More)
Cardinal polysplines of order p on annuli are functions in C2p−2 (Rn \ {0}) which are piecewise polyharmonic of order p such that ∆p−1S may have discontinuities on spheres in Rn, centered at the origin and having radii of the form ej , j ∈ Z. The main result is an interpolation theorem for cardinal polysplines where the data are given by sufficiently smooth(More)
Let LN+1 be a linear differential operator of order N + 1 with constant coefficients and real eigenvalues 1, . . . , N+1, let E( N+1) be the space of all C∞-solutions of LN+1 on the real line. We show that for N 2 and n = 2, . . . , N , there is a recurrence relation from suitable subspaces En to En+1 involving real-analytic functions, andwithEN+1=E( N+1)(More)
Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form Z× aZn having practical importance. The main purpose of the paper is to consider the behavior of the polyharmonic interpolation splines Ia on such grids for the(More)
We continue the study of a new family of multivariate wavelets which are obtained by "polyharmonic subdivision". We provide the results of experiments considering the distribution of the wavelet coefficients for the Lena image and for astronomical images. The main purpose of this investigation is to find a clue for proper quantization algorithms.