The asymptotic behavior for entropy numbers of general Fourier multiplier operators of
multiple series with respect to an abstract complete orthonormal system {ϕ m} m∈ N 0 d on …

We study volumes of sections of convex origin-symmetric bodies in R n induced by
orthonormal systems on probability spaces. The approach is based on volume estimates of …

The main objective of this article is to present new results on optimal reconstruction of
function classes on probability spaces (Ω, A, ν) in the standard L q spaces. We consider the …

In this paper, we investigate entropy numbers of multiplier operators Λ={λ k} k∈ Z d and
Λ∗={λ k∗} k∈ Z d, Λ, Λ∗: L p (T d)→ L q (T d) on the d-dimensional torus T d, where λ k= λ …

Let V and W be any convex and origin-symmetric bodies in R n. Assume that for some A∈
LR n→ R n, det A≠ 0, V is contained in the ellipsoid A− 1 B 2 n, where B 2 n is the unit …

Abstract Estimates for Kolmogorov and Gelfand n-widths of multiplier operators of multiple
Walsh series are obtained. Upper and lower bounds are established for n-widths of general …

We study volumes of sections of convex origin-symmetric bodies in $\mathbb {R}%^{n} $
induced by orthonormal systems on probability spaces. The approach is based on volume …

In this work we investigate n-widths of multiplier operators Λ∗ and Λ, defined for functions on
the complex sphere Ω d of ℂ d, associated with sequences of multipliers of the type {λ m, n∗} …

Fixed a continuous kernel K on the $ d $-dimensional torus, we consider a generalization of
the univariate $ sk $-spline to the torus, associated with the kernel K. It is proved an estimate …

We consider an important class of derivative contracts written on multiple assets which are
traded on a wide range of financial markets. More specifically, we are interested in …