Geodesic
Best recovery of the Laplace operator of a~function from incomplete spectral data
Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 569-580

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is concerned with the problem of best recovery for a fractional power of the Laplacian of a smooth function on $\mathbb R^d$ from an exact or approximate Fourier transform for it, which is known on some convex subset of $\mathbb R^d$. A series of optimal recovery methods is constructed. Information about the Fourier transform outside some ball centred at the origin proves redundant — it is not used by the optimal methods. These optimal methods differ in the way they ‘process’ key information. Bibliography: 12 titles.
Keywords: Laplace operator, optimal recovery, extremal problem
Mots-clés : Fourier transform. 
@article{SM_2012_203_4_a5,
     author = {G. G. Magaril-Il'yaev and E. O. Sivkova},
     title = {Best recovery of the {Laplace} operator of a~function from incomplete spectral data},
     journal = {Sbornik. Mathematics},
     pages = {569--580},
     publisher = {mathdoc},
     volume = {203},
     number = {4},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_4_a5/}
}
TY  - JOUR
AU  - G. G. Magaril-Il'yaev
AU  - E. O. Sivkova
TI  - Best recovery of the Laplace operator of a~function from incomplete spectral data
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 569
EP  - 580
VL  - 203
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_4_a5/
LA  - en
ID  - SM_2012_203_4_a5
ER  - 
%0 Journal Article
%A G. G. Magaril-Il'yaev
%A E. O. Sivkova
%T Best recovery of the Laplace operator of a~function from incomplete spectral data
%J Sbornik. Mathematics
%D 2012
%P 569-580
%V 203
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2012_203_4_a5/
%G en
%F SM_2012_203_4_a5
G. G. Magaril-Il'yaev; E. O. Sivkova. Best recovery of the Laplace operator of a~function from incomplete spectral data. Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 569-580. http://geodesic.mathdoc.fr/item/SM_2012_203_4_a5/