5 papers
Uniform approximations by Fourier sums on classes of convolutions of periodic functions
A. S. Serdyuk, T. A. Stepanyuk
We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of -periodic functions, which are represented by convolutions…
Poissonian pair correlation on manifolds via the heat kernel
Peter J. Grabner, Tetiana A. Stepanyuk
We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earl…
Hyperuniform point sets on flat tori: deterministic and probabilistic aspects
Tetiana Stepanyuk
In this paper we study hyperuniformity on flat tori. Hyperuniform point sets on the unit sphere have been studied by J.~Brauchart, P.~Grabner, W.~Kusner and J.~Ziefle. It is shown…
Estimates for logarithmic and Riesz energies for spherical -designs
Tetiana Stepanyuk
In this paper we find asymptotic equalities for the discrete logarithmic energy of sequences of well separated spherical -designs on the unit sphere ${\mathbb{S}^{d}\subset\math…
Order estimates of best orthogonal trigonometric approximations of classes of infinitely differentiable functions
Tetiana Stepanyuk
In this paper we establish exact order estimates for the best uniform orthogonal trigonometric approximations of the classes of -periodic functions, whose -derivatives b…