Best recovery of the Laplace operator of a function from incomplete spectral data

This paper is concerned with the problem of best recovery for a fractional power of the Laplacian of a smooth function on R{sup d} from an exact or approximate Fourier transform for it, which is known on some convex subset of R{sup d}. A series of optimal recovery methods is constructed. Information...

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Bibliographic Details
Published in:Sbornik. Mathematics 2012-04, Vol.203 (4)
Main Authors: Magaril-Il'yaev, Georgii G, Sivkova, Elena O
Format: Article
Language:English
Subjects:
APPROXIMATIONS
CALCULATION METHODS
EXACT SOLUTIONS
FOURIER TRANSFORMATION
FUNCTIONS
INFORMATION THEORY
INTEGRAL TRANSFORMATIONS
LAPLACIAN
MATHEMATICAL MANIFOLDS
MATHEMATICAL METHODS AND COMPUTING
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
SMOOTH MANIFOLDS
TRANSFORMATIONS
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Summary:This paper is concerned with the problem of best recovery for a fractional power of the Laplacian of a smooth function on R{sup d} from an exact or approximate Fourier transform for it, which is known on some convex subset of R{sup 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.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM2012V203N04ABEH004235;COUNTRYOFINPUT:INTERNATIONALATOMICENERGYAGENCY(IAEA)