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pro vyhledávání: '"Stepanyuk, Tetiana A."'
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 earlier work by Grepstad and Larcher, Aistleitner, Lachmann, and Pausinger
Externí odkaz:
http://arxiv.org/abs/1904.08286
Autor:
Stepanyuk, Tetiana
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 that point sets which are hyperuniform for large balls, small balls or
Externí odkaz:
http://arxiv.org/abs/1902.02973
Autor:
Stepanyuk, Tetiana
In this paper we find asymptotic equalities for the discrete logarithmic energy of sequences of well separated spherical $t$-designs on the unit sphere ${\mathbb{S}^{d}\subset\mathbb{R}^{d+1}}$, $d\geq2$. Also we establish exact order estimates for d
Externí odkaz:
http://arxiv.org/abs/1901.00437
Autor:
Stepanyuk, Tetiana
In this paper we establish exact order estimates for the best uniform orthogonal trigonometric approximations of the classes of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}$, $1\leq p<\infty$, in t
Externí odkaz:
http://arxiv.org/abs/1812.06475
Autor:
Grabner, Peter, Stepanyuk, Tetiana
Publikováno v:
Journal of Approximation Theory 2019
In this paper we make a comparison between certain probabilistic and deterministic point sets and show that some deterministic constructions (spherical $t$-designs) are better or as good as probabilistic ones. We find asymptotic equalities for the di
Externí odkaz:
http://arxiv.org/abs/1803.08901
Autor:
Grabner, Peter, Stepanyuk, Tetiana
Publikováno v:
Journal of Complexity 2019
In this paper we study the worst-case error of numerical integration on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$, $d\geq2$, for certain spaces of continuous functions on $\mathbb{S}^{d}$. For the classical Sobolev spaces $\mathbb{H}^s(
Externí odkaz:
http://arxiv.org/abs/1801.05474
Publikováno v:
In Journal of Approximation Theory March 2019 239:128-143
Autor:
Stepanyuk, Tetiana A.1,2,3 (AUTHOR) stepaniuk.tet@gmail.com
Publikováno v:
Constructive Approximation. Oct2020, Vol. 52 Issue 2, p313-339. 27p.
Autor:
Serdyuk, Anatoly S.1 serdyuk@imath.kiev.ua, Stepanyuk, Tetiana A.2 tania_stepaniuk@ukr.net
Publikováno v:
Bulletin de la Société des Sciences et des Lettres de Lodz. 2018, Vol. 68 Issue 2, p45-51. 7p.
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