Optimal recovery and generalized Carlson inequality for weights with symmetry properties
Numerical Analysis
2023-03-21 v1 Numerical Analysis
Functional Analysis
Abstract
The paper concerns problems of the recovery of operators from noisy information in weighted -spaces with homogeneous weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type inequalities with several weights and problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the -metric.
Keywords
Cite
@article{arxiv.2303.10355,
title = {Optimal recovery and generalized Carlson inequality for weights with symmetry properties},
author = {K. Yu. Osipenko},
journal= {arXiv preprint arXiv:2303.10355},
year = {2023}
}