Integral norm discretization and related problems
Numerical Analysis
2019-11-01 v3
Abstract
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite dimensional spaces. Also, discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of the multivariate trigonometric polynomials with frequencies from a finite set with fixed cardinality. Both new results and a survey of known results are presented.
Cite
@article{arxiv.1807.01353,
title = {Integral norm discretization and related problems},
author = {F. Dai and A. Prymak and V. N. Temlyakov and S. Tikhonov},
journal= {arXiv preprint arXiv:1807.01353},
year = {2019}
}