Some results related to the Logvinenko-Sereda theorem
By O. Kovrizhkin. 2000
84 citations recorded by the source corpus.
We prove several results related to the theorem of Logvinenko and Sereda on determining sets for functions with Fourier transforms supported in an interval. We obtain a polynomial instead of exponential bound in this theorem, and we extend it to the case of functions with Fourier transforms supported in the union of a bounded number of intervals. The same results hold in all dimensions.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/6242659e0baf245fa2f26175a14d9fb5735115f1
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In Applied Mathematics
- K. Pravda-Starov
- Michela Egidi
- Ivan Veselić
- Karine Beauchard
- Philippe Jaming
- Eduardo Cerpa
- Enrique Zuazua
- Olivier Glass
Citations in the corpus
- Sharp geometric condition for null-controllability of the heat equation on $$\mathbb {R}^d$$Rd and consistent estimates on the control cost (2017, background): “nenko & Sereda and Kacnel’son in [LS74, Kac73]. Kovrijkine [Kov01, Kov00] has turned these qualitative equivalence statements into a quantitative estimate. Theorem 7 (Logvinenko-Sereda theorem by [Kov01]). Let f P L2pRdq and assume that suppfˆ Ă J, where J is a parallelepiped with sides parallel”
- Spectral estimates for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations (2018, background): “As in [30], the proof is only written with full details in the onedimensional case with hints for its extension to the multi-dimensional one following some ideas of Nazarov [36], the proof given in Section 3.”