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Heisenberg Uniqueness Pairs for the Finitely Many Parallel Lines with an Irregular Gap

Giri, DK and Srivastava, RK (2022) Heisenberg Uniqueness Pairs for the Finitely Many Parallel Lines with an Irregular Gap. In: Journal of Fourier Analysis and Applications, 28 (2).

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Official URL: https://doi.org/10.1007/s00041-022-09932-8


Let X(�) be the space of all finite Borel measure μ in R2 which is supported on the smooth curve� and absolutely continuous with respect to the arc length on �. For � � R2, the pair (� , �) is called a Heisenberg uniqueness pair for X(�) if any μ� X(�) satisfies μ | �= 0 , implies μ= 0. We prove a characterization of the Heisenberg uniqueness pairs corresponding to finitely many parallel lines with an irregular gap. We observe that the size of the determining sets � for X(�) depends on the number of lines and their irregular distribution that further relates to a phenomenon of the interlacing of certain trigonometric polynomials. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Item Type: Journal Article
Publication: Journal of Fourier Analysis and Applications
Publisher: Birkhauser
Additional Information: The copyright for this article belongs to Birkhauser
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 17 May 2022 06:54
Last Modified: 17 May 2022 06:54
URI: https://eprints.iisc.ac.in/id/eprint/71763

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