Speaker
Il'dar Musin
(Institute of Mathematics with Computer Centre of Ufa Scientific Centre of RAS)
Description
Classes of ultradifferentiable functions are classically defined by imposing growth conditions on the derivatives of the functions. Following this approach we consider a Fr\'echet-Schwartz space of infinitely differentiable functions on a closure of a bounded convex domain of multidimensional real space with uniform bounds on their partial derivatives. The main aim is to obtain Paley-Wiener-Schwartz type theorem connecting properties of linear continuous functionals on this space with the behaviour of their Fourier-Laplace transforms. Very similar problems were considered by M. Neymark, B.A. Taylor, M. Langenbruch, A.V. Abanin. Also some applications of this theorem to PDE and their systems will be given.
Primary author
Il'dar Musin
(Institute of Mathematics with Computer Centre of Ufa Scientific Centre of RAS)
