Optimal recovery in weighted spaces with homogeneous weights

Optimal recovery in weighted spaces with homogeneous weights

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 problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are o...

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Veröffentlicht in:Sbornik. Mathematics 2022-03, Vol.213 (3), p.385-411
1. Verfasser: Osipenko, K. Yu
Format: Artikel
Sprache:eng
Schlagworte:
Carlson’s inequality
Differential equations
Fourier transform
Fourier transforms
linear operator
Operators (mathematics)
optimal recovery
Recovery
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Beschreibung
Zusammenfassung: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 problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of the Laplace operator from a noisy Fourier transform in the -metric. Bibliography: 30 titles.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM9475