The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the
engineering, mathematical, and scientific communities with significant developments in …

In this note we estimate the asymptotic rates for the L 2-error decay and the storage cost
when approximating 2 π-periodic, d-variate functions from isotropic and mixed Sobolev …

This book is a survey on multivariate approximation. The 20th century was a period of
transition from univariate problems to multivariate problems in a number of areas of …

Evaluating treatments received by one population for application to a different target
population of scientific interest is a central problem in causal inference from observational …

We investigate the approximation of d-variate periodic functions in Sobolev spaces of
dominating mixed (fractional) smoothness s> 0 s> 0 on the d-dimensional torus, where the …

In this paper, we present algorithms for the approximation of multivariate periodic functions
by trigonometric polynomials. The approximation is based on sampling of multivariate …

We consider the approximate recovery of multivariate periodic functions from a discrete set
of function values taken on a rank-1 lattice. Moreover, the main result is the fact that any (non …

Using tools from the theory of operator ideals and s-numbers, we develop a general
approach to transfer estimates for L 2-approximation of Sobolev functions into estimates for …

In the last 20 years a whole hierarchy of notions of tractability was proposed and analyzed
by several authors. These notions are used to classify the computational hardness of …

In this paper, we reveal a new connection between approximation numbers of periodic
Sobolev type spaces, where the smoothness weights on the Fourier coefficients are induced …