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Andrew Bakan: Several open problems for the Klein-Gordon equation in unbounded domains

Tid: On 2016-11-02 kl 13.15

Plats: 3721

Medverkande: Andrew Bakan, Institute of Mathematics, Natl. Acad. Sci. of Ukraine, Kyiv

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In the first part of this talk we study time-periodic (with a period T) solutions i (t, x) and u (t,x) of the one-dimensional telegraph equations. For any fixed moment t of time we write explicitly an integral operator which reconstructs the values of i (t, x) and u (t,x) for all x by their values on an arbitrary segment of x of the length T/\sqrt{CL}.

In the second part, we examine all those continuous solutions of the one-dimensional Klein-Gordon equation in unbounded domain which are bounded there by exp a (|x|+|y|) with a certain a>0. We prove that the boundary conditions for such kind of solutions cannot be assigned arbitrarily. This fact allows to state the lattice-cross interpolation problem where the recent results of Hedenmalm and Montes-Rodriguez (2014), and of Radchenko and Viazovska (2016) can be effectively used.