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 $\mathbb R^d$ 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.
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