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Article history: Received 9 September 2012 Received in revised form 19 December 2013 Accepted 29 December 2013 Available online xxxx Communicated by Peter Oswald

- J. M. Aldaz, Ognyan Kounchev, Hermann Render
- Numerische Mathematik
- 2009

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 Bernsteinâ€¦ (More)

- Ognyan Kounchev, Hermann Render
- Journal of Approximation Theory
- 2005

Cardinal polysplines of order p on annuli are functions in C2pâˆ’2 (Rn \ {0}) which are piecewise polyharmonic of order p such that âˆ†pâˆ’1S may have discontinuities on spheres in Rn, centered at the origin and having radii of the form ej , j âˆˆ Z. The main result is an interpolation theorem for cardinal polysplines where the data are given by sufficiently smoothâ€¦ (More)

- J. M. Aldaz, Ognyan Kounchev, Hermann Render
- Journal of Approximation Theory
- 2007

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 Câˆž-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)â€¦ (More)

- Ognyan Kounchev, Michael J. Wilson
- IMA Conference on the Mathematics of Surfaces
- 2003

We apply new methods based on Partial Differential Equations techniques (polysplines) to the visualization of the heart surface.

- Ognyan Kounchev
- 2004

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 ZÃ— 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 theâ€¦ (More)

- Ognyan Kounchev
- 2008

A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudopositive definite functional (subject to some reasonable restrictions) there exists a representing pseudo-positive measure. The second main result is a characterization of determinacy in the class of equivalentâ€¦ (More)

- Ognyan Kounchev, Damyan Kalaglarsky
- CompSysTech
- 2010

We introduce a new family of multivariate wavelets which are obtained by "polyharmonic subdivision". They generalize directly the original compactly supported Daubechies wavelets.

- Ognyan Kounchev, Damyan Kalaglarsky
- CompSysTech
- 2011

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.