arXiv subjects

A. Yu. Ulitskaya

Publications and source records attributed to A. Yu. Ulitskaya.

2 recordsLinked to original sources

arXiv2022

Fourier analysis in spaces of shifts

In this paper, we develop a continual analog of decomposition over orthogonal bases in spaces generated by equidistant shifts of a single function. By doing so, we obtain an explicit expression for best approximation by spaces of shifts in $L_2(\mathbb{R})$. The result is formulated in terms of classical Fourier transform and tends to have various applications in approximation by spaces of shifts and, in particular, in spline approximation.

math.CA↗

arXiv2019

Optimal subspaces for mean square approximation of classes of differentiable functions with boundary conditions

In this paper, we specify a set of optimal subspaces for $L_2$ approximation of three classes of functions in the Sobolev space $W^{(r)}_2$, defined on a segment and subject to certain boundary conditions. All of these subspaces are generated by equidistant shifts of a single function. In particular, we indicate optimal spline spaces of all degrees $d\geqslant r-1$ with uniform knots.

math.CA↗