A generalized Fourier transform by means of change of variables within multilinear approximation

Abstract The paper deals with approximations of periodic functions that play a significant role in harmonic analysis. approach revisits the trigonometric polynomials, seen as combinations functions, and proposes to extend class models combined wider functions. key here is use structured have low complexity, suitable functional representation adapted parametrizations for approximation. Such enables approximate multivariate few eventually random samples. new parametrization determined automatically greedy procedure, rank format used approximation associated each parametrization. A supervised learning algorithm function multiple variables tree-based tensor format, particular Tensor Train format. Adaptive strategies using statistical error estimates are proposed selection underlying bases ranks Tensor-Train method applied estimation wall pressure flow over cylinder range medium Reynolds numbers which we observe two regimes: laminar vortex shedding boundary layer turbulent wake (sub-critic regime). automatic re-parametrization take into account specific feature pressure.