52 citations · 123 across the 34 of their papers we have counts for
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On Polyharmonic Interpolation
Werner Haussmann, Ognyan Kounchev
In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic…
On a new multivariate sampling paradigm and a polyspline Shannon function
Ognyan Kounchev, Hermann Render
In the monograph Kounchev, O. I., Multivariate Polysplines. Applications to Numerical and Wavelet Analysis, Academic Press, San Diego-London, 2001, and in the paper Kounchev O., Re…
Multidimensional Chebyshev Systems - just a definition
Ognyan Kounchev
We provide a definition of Multidimensional Chebyshev Systems of order N which is satisfied by the solutions of a wide class of elliptic equations of order 2N. This definition gene…
Bernstein operators for exponential polynomials
J. M. Aldaz, O. Kounchev, H. Render
Let be a linear differential operator with constant coefficients of order and complex eigenvalues . Assume that the set of all solutions of the equ…
Bernstein Operators for Extended Chebyshev Systems
J. M. Aldaz, O. Kounchev, H. Render
Let be an extended Chebyshev space of dimension . Suppose that is strictly positive and has the property that $…
Shape preserving properties of generalized Bernstein operators on Extended Chebyshev spaces
J. M. Aldaz, O. Kounchev, H. Render
We study the existence and shape preserving properties of a generalized Bernstein operator fixing a strictly positive function , and a second function such t…
A moment problem for pseudo-positive definite functionals
Ognyan Kounchev, Hermann Render
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to s…