2,748 research outputs found
Almost periodic solutions of periodic linear partial functional differential equations
We study conditions for the abstract periodic linear functional differential
equation to have almost periodic with the same
structure of frequencies as . The main conditions are stated in terms of the
spectrum of the monodromy operator associated with the equation and the
frequencies of the forcing term . The obtained results extend recent results
on the subject. A discussion on how the results could be extended to the case
when depends on is given.Comment: 17 page
Integrable discrete Schrodinger equations and a characterization of Prym varieties by a pair of quadrisecants
We prove that Prym varieties are characterized geometrically by the existence
of a symmetric pair of quadrisecant planes of the associated Kummer variety. We
also show that Prym varieties are characterized by certain (new)
theta-functional equations. For this purpose we construct and study a
difference-differential analog of the Novikov-Veselov hierarchy
Weighted Dirac combs with pure point diffraction
A class of translation bounded complex measures, which have the form of
weighted Dirac combs, on locally compact Abelian groups is investigated. Given
such a Dirac comb, we are interested in its diffraction spectrum which emerges
as the Fourier transform of the autocorrelation measure. We present a
sufficient set of conditions to ensure that the diffraction measure is a pure
point measure. Simultaneously, we establish a natural link to the theory of the
cut and project formalism and to the theory of almost periodic measures. Our
conditions are general enough to cover the known theory of model sets, but also
to include examples such as the visible lattice points.Comment: 44 pages; several corrections and improvement
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