Local and global phaseless sampling in real spline spaces
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- by Wenchang Sun;
- Math. Comp. 90 (2021), 1899-1929
- DOI: https://doi.org/10.1090/mcom/3620
- Published electronically: March 17, 2021
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Abstract:
We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on the whole line from infinitely many unsigned samples. In both cases, we give characterizations for a set of points to be a phaseless sampling set, at which any nonseparable function is determined up to a sign on an interval or on the whole line by its unsigned sampled values. Moreover, for the case of local recovery, we also study the almost phaseless sampling and give a necessary and sufficient condition for a set of points to admit a local recovery for almost all functions.References
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Bibliographic Information
- Wenchang Sun
- Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
- ORCID: 0000-0002-5841-9950
- Email: sunwch@nankai.edu.cn
- Received by editor(s): April 6, 2019
- Received by editor(s) in revised form: February 5, 2020, and December 3, 2020
- Published electronically: March 17, 2021
- Additional Notes: This work was partially supported by the National Natural Science Foundation of China (11525104, 11531013 and 11761131002).
- © Copyright 2021 American Mathematical Society
- Journal: Math. Comp. 90 (2021), 1899-1929
- MSC (2020): Primary 42C15; Secondary 46C05, 94A20
- DOI: https://doi.org/10.1090/mcom/3620
- MathSciNet review: 4273119