Base change problems for generalized Walsh series and multivariate numerical integration (Q1305105)

Walsh functions over a finite abelian group [see \textit{G. Larcher}, \textit{H. Niederreiter}, and \textit{W. Ch. Schmid}, Monatsh. Math. 121, 231-253 (1996; Zbl 0876.11042)] play an important role for various digital lattice rules in multivariate numerical integration. The authors consider the following problem: Assume that a function \(f\) can be represented by a Walsh series over a group \(G_1\) with a certain speed of convergence. What can be said about the speed of convergence of the Walsh series of \(f\) over another group \(G_2\)? The authors present some results, partly best possible ones. Answers to this base change problem are essential for error estimates of numerical integration. A connection to the digital differentiability of functions and applications in multivariate numerical integration are given. Finally, some open problems are stated.