52 citations · 123 across the 34 of their papers we have counts for
36 papers
On the log-concavity of the composite Bessel function
O. Kounchev, H. Render
For a twice differentiable function define It is well known that the posit…
Fast algorithms for interpolation with clamped -splines of order four
O. Kounchev, H. Render, G. Simeonov +1
Interpolation and smoothing using cubic and generalized splines are fundamental tools in data analysis and statistical modeling. Recently, fast computational algorithms were develo…
On the critical length conjecture for spherical Bessel functions in CAGD
Ognyan Kounchev, Hermann Render
A conjecture of J.M. Carnicer, E. Mainar and J.M. Peña states that the critical length of the space generated by the functions and fo…
Inequalities for exponential polynomials with applications to moment sequences
Ognyan Kounchev, Hermann Render, Tsvetomir Tsachev
Let be the unique solution of the differential operator such that …
Error estimates for harmonic and biharmonic interpolation splines with annular geometry
Ognyan Kounchev, Hermann Render, Tsvetomir Tsachev
The main result in this paper is an error estimate for interpolation biharmonic polysplines in an annulus , with respect to a partition by concentric a…
Fast algorithms for interpolation with L-splines for differential operators L of order 4 with constant coefficients
Ognyan Kounchev, Hermann Render, Tsvetomir Tsachev
In the classical theory of cubic interpolation splines there exists an algorithm which works with only arithmetic operations. Also, the smoothing cubic splines m…
Error bounds for interpolation with piecewise exponential splines of order two and four
Ognyan Kounchev, Hermann Render
Explicit pointwise error bounds for the interpolation of a smooth function by piecewise exponential splines of order four are given. Estimates known for cubic splines are extended…
Wavelet Analysis of Big Data in the Global Investigation of Magnetic Field Variations in Solar-Terrestrial Physics
Bozhidar Srebrov, Ognyan Kounchev, Georgi Simeonov
We provide a Wavelet analysis of Big Data in Solar Terrestrial Physics. In order to explain and predict the dynamics of the geomagnetic phenomena we analyze high frequency time ser…
A symmetry property for polyharmonic functions vanishing on equidistant hyperplanes
Ognyan Kounchev, Hermann Render
Let be a polyharmonic function of order defined on the strip satisfying the growth condition $$ \sup_{t\in K}\lef…
A new cubature formula with weight functions on the disc, with error estimates
O. Kounchev, H. Render
We introduce a new type of cubature formula for the evaluation of an integral over the disk with respect to a weight function. The method is based on an analysis of the Fourier ser…
Discrete Hybrid Polyharmonic Cubature Formulas with weight on the disc. with error bounds
O. Kounchev, H. Render
This paper is a second part of our study of the Discrete Polyharmonic Cubature Formulas on the disc. It completes our study and provides a satisfactory cubature formula in terms of…
Klein-Dirac Quadric and Multidimensional Toda Lattice via Pseudo-positive Moment Problem
Sergio Albeverio, Ognyan Kounchev
In 1974 Jürgen Moser has shown that the classical Moment Problem plays a fundamental role for the theory of completely integrable systems, by proving that the simplest case of the…
Regularity of generalized Daubechies wavelets reproducing exponential polynomials
N. Dyn, O. Kounchev, D. Levin +1
We investigate non-stationary orthogonal wavelets based on a non-stationary interpolatory subdivision scheme reproducing a given set of exponentials. The construction is analogous…
Polyharmonic functions of infinite order on annular regions
Ognyan Kounchev, Hermann Render
Polyharmonic functions f of infinite order and type τ on annular regions are systematically studied. The first main result states that the Fourier-Laplace coefficients f_{k,l}(r) o…
Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas
Ognyan Kounchev, Hermann Render
In the present paper we introduce a new concept of Hardy type space naturally defined on the Klein-Dirac quadric. We study different properties of the functions belonging to these…
Compressive Sensing for Polyharmonic Subdivision Wavelets With Applications to Image Analysis
Ognyan Kounchev, Damyan Kalaglarsky
We apply successfully the Compressive Sensing approach for Image Analysis using the new family of Polyharmonic Subdivision wavelets. We show that this approach provides a very effi…
Quantization Opportunities for Polyharmonic Subdivision Wavelets Applied to Astronomical Images
Ognyan Kounchev, Damyan Kalaglarsky
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…
Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas
Ognyan Kounchev, Hermann Render
The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the an…
Polyharmonicity and algebraic support of measures
Ognyan Kounchev, Hermann Render
We introduce a multivariate Markov transform which generalizes the well-known one-dimensional Stieltjes transform from the Moment problem and Spectral theory. Our main result state…
Padé approximation for a multivariate Markov transform
Ognyan Kounchev, Hermann Render
Methods of Padé approximation are used to analyse a multivariate Markov transform which has been recently introduced by the authors, and which is generalizing the well-known in Spe…
Holomorphic Continuation via Laplace-Fourier series
O. Kounchev, H. Render
Let be the ball in the euclidean space with center 0 and radius and let be a complex-valued, infinitely differentiable function on We show…
Multidimensional Chebyshev spaces, hierarchy of infinite-dimensional spaces and Kolmogorov-Gelfand widths
O. Kounchev
Recently the theory of widths of Kolmogorov (especially of Gelfand widths) has received a great deal of interest due to its close relationship with the newly born area of Compresse…
On a hierarchy of infinite-dimensional spaces and related Kolmogorov-Gelfand widths
Ognyan Kounchev
Recently the theory of widths of Kolmogorov-Gelfand has received a great deal of interest due to its close relationship with the newly born area of Compressed Sensing. It has been…
Infinite-dimensional generalization of Kolmogorov widths
Ognyan Kounchev
Recently the theory of widths of Kolmogorov-Gelfand has received a great deal of interest due to its close relationship with the newly born area of Compressive Sensing in Signal Pr…