Nonlinear approximation and its applications

I first met Wolfgang Dahmen in 1974 in Oberwolfach. He looked like a high school student to me but he impressed everyone with his talk on whether polynomial operators could produce both polynomial and spectral orders of approximation. We became the best of friends and frequent collaborators. While Wolfgang’s mathematical contributions spread across many disciplines, a major thread in his work has been the exploitation of nonlinear approximation. This article will reflect on Wolfgang’s pervasive contributions to the development of nonlinear approximation and its application. Since many of the contributions in this volume will address specific application areas in some details, my thoughts on these will be to a large extent anecdotal.