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).
This is the latest version of this item.
Preview |
Text
Download (685kB) | Preview |
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 |
Available Versions of this Item
-
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]