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Order Estimates for the Best Approximations and Approximations by Fourier Sums in the Classes of Convolutions of Periodic Functions of Low Smoothness in the Uniform Metric
We obtain the exact-order estimates for the best uniform approximations and uniform approximations by Fourier sums in the classes of convolutions of periodic functions from the unit balls of theExpand
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Comparison of probabilistic and deterministic point sets on the sphere
We find asymptotic equalities for the discrete Riesz s -energy of sequences of well separated t -designs on the unit sphere S d ⊂ R d + 1 , d ≥ 2 . Expand
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Comparison of probabilistic and deterministic point sets
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 asExpand
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On the Approximation of the Classes WβrHα$$ {W}_{\beta}^r{H}^{\alpha } $$ by Biharmonic Poisson Integrals
We obtain asymptotic equalities for the least upper bounds of deviations of the biharmonic Poisson integrals of functions of the classes WβrHα$$ {W}_{\beta}^r{H}^{\alpha } $$ in the case where r > 2,Expand
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Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension
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 $\mathBB{S]^{d}$. Expand
Approximation of the Classes of Generalized Poisson Integrals by Fourier Sums in Metrics of the Spaces LS
In metrics of the spaces Ls, 1 ≤ s ≤ 1, we establish asymptotic equalities for the upper bounds of approximations by Fourier sums in the classes of generalized Poisson integrals of periodic functionsExpand
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Poissonian pair correlation on manifolds via the heat kernel.
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 byExpand
Approximation of Functions from the Classes WβrHα$$ {W}_{\beta}^r{H}^{\alpha } $$ by Weierstrass Integrals
We study the asymptotic behavior of the least upper bounds of the approximations of functions from the classes WβrHα$$ {W}_{\beta}^r{H}^{\alpha } $$ by Weierstrass integrals in the uniform metric.
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