Fourier transform, null variety, and Laplacian's eigenvalues

Benguria, R., Levitin, M. ORCID: https://orcid.org/0000-0003-0020-3265 and Parnovski, L. (2009) Fourier transform, null variety, and Laplacian's eigenvalues. Journal of Functional Analysis, 257 (7). pp. 2088-2123. ISSN 0022-1236 doi: 10.1016/j.jfa.2009.06.022

Abstract/Summary

We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/16152
Identification Number/DOI	10.1016/j.jfa.2009.06.022
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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