This book provides a systematic survey of classical and recent results on hyperbolic cross
approximation. Motivated by numerous applications, the last two decades have seen great …

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

Lattice rules are particular instances of quasi-Monte Carlo rules for numerical integration of
functions over the 𝑑-dimensional unit cube [0, 1] 𝑑, where the emphasis lies on high …

We construct a least squares approximation method for the recovery of complex-valued
functions from a reproducing kernel Hilbert space on D⊂ R d. The nodes are drawn at …

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 …

We propose an approximation method for high-dimensional 1-periodic functions based on
the multivariate ANOVA decomposition. We provide analysis of classical ANOVA …

Riemann theta functions play a crucial role in the field of nonlinear Fourier analysis, where
they are used to realize inverse nonlinear Fourier transforms for periodic signals. The …

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 …

The paper discusses the construction of high dimensional spatial discretizations for arbitrary
multivariate trigonometric polynomials, where the frequency support of the trigonometric …

In this work, we consider the approximate reconstruction of high-dimensional periodic
functions based on sampling values. As sampling schemes, we utilize so-called …