caa a22 4500 605525730 CHVBK 20210128100800.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2490-6 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2490-6 Sivkova E. Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Moscow, Russia aut Best Recovery of the Laplace Operator of a Function and Sharp Inequalities [Elektronische Daten] [E. Sivkova] The paper is concerned with the problem of optimal recovery of fractional powers of the Laplace operator in the uniform norm on the multivariate generalized Sobolev class of functions from incomplete data on the Fourier transform of these functions on a ball of radius r centered at the origin. An optimal recovery method is constructed, and a number r ^ $$ \widehat{r} $$ > 0 is specified such that for r ≤ r ^ $$ \widehat{r} $$ the method makes use of all the information on the Fourier transform, smoothing thereof; and if r > r ^ $$ \widehat{r} $$ , then the information on the Fourier transform proves superfluous and hence is not used by the optimal method. For fractional powers of the Laplace operator, a sharp inequality is proved. This inequality turns out to be closely related to the recovery problem and is an analogue of Kolmogorov-type inequalities for derivatives. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 130-137 1072-3374 209:1<130 2015 209 10958 https://doi.org/10.1007/s10958-015-2490-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2490-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sivkova E. Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 130-137 1072-3374 209:1<130 2015 209 10958