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math.SP2008★ 1 cited
Fourier transform, null variety, and Laplacian's eigenvalues
Rafael Benguria, Michael Levitin, Leonid Parnovski
We consider a quantity -- the distance to the origin from the null variety of the Fourier transform of the characteristic function of . We conjecture, firstly, that $κ(Ω)…
math.SP2008
On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities
Lyonell Boulton, Michael Levitin, Marco Marletta
We prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.…