English

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 LqL_q-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 LpL_p-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}
}