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On best localized bandlimited functions |
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| Authors: | S Norvidas |
| Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania |
| Abstract: | Let, for σ > 0,
be the set of complex functions f ∈ L
1 (ℝ) with the Fourier transforms
vanishing outside the interval −σ; σ]. In this paper, we study the problem of the best approximation of the Dirac function δ (which has the Fourier transform with widest support supp
) by functions
. More precisely, we consider the quantity inf
and its extremal functions
.
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Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 548–564, October–December, 2006. |
| Keywords: | Fourier transform bandlimited functions best localization spectral synthesis sets Bohr inequality Poisson summation formula sine-type entire functions |
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