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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Identification Number : 10.1007/s00041-021-09875-6

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.

Item Type: Article
Language: English
Date: August 2021
Refereed: Yes
Place of Publication: Boca Raton
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 22 Jun 2021 08:42
Last Modified: 01 Feb 2022 12:47
OAI Identifier: oai:tse-fr.eu:125752
URI: https://publications.ut-capitole.fr/id/eprint/43634

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