Gaillac, Christophe and Gautier, Eric (2021) Estimates for the SVD of the Truncated Fourier Transform on L2(cosh(b.)) and Stable Analytic Continuation. Journal of Fourier Analysis and Applications, vol.27 (n°4).

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Abstract

The Fourier transform truncated on [−c, c] is usually analyzed when acting on
L
2
(−1/b, 1/b) and its right-singular vectors are the prolate spheroidal wave functions. This
paper considers the operator acting on the larger space L
2
(cosh(b·)) on which it remains
injective. We give nonasymptotic upper and lower bounds on the singular values with similar
qualitative behavior in m (the index), b, and c. The lower bounds are used to obtain rates
of convergence for stable analytic continuation of possibly nonbandlimited functions which
Fourier transform belongs to L
2
(cosh(b·)). We also derive bounds on the sup-norm of the
singular functions. Finally, we provide a numerical method to compute the SVD and apply it
to stable analytic continuation when the function is observed with error on an interval.

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• Estimates for the SVD of the truncated fourier transform on L2(cosh(b.)) and stable analytic continuation. (deposited 20 May 2019 08:17)
  • Estimates for the SVD of the Truncated Fourier Transform on L2(cosh(b.)) and Stable Analytic Continuation. (deposited 22 Jun 2021 08:42) [Currently Displayed]