ON THE NEW THEORY OF LINEAR DYNAMICAL SYSTEMS
Time and place
1 PM on Thursday, May 8th, 2014; NAC 6/113
ELI GLASNER (TEL AVIV UNIVERSITY)
Abstract
Can a linear transformation exhibit chaotic behavior? Can a comet have the property that for every region U of space there is a time T such that up to time nT the comet visits U at least n times? Can a standard Gaussian stochastic process be modeled on Hilbert space? Does every bounded linear operator on Hilbert space admit a proper closed invariant subspace? Assuming the Riemann hypothesis, is the orbit of the Riemann zeta under the semigroup of translations T_tf(z) = f(z +it) dense in the space of entire functions which do not vanish on the critical strip {z: 1/2 < Re(z) < 1}?
These seemingly unrelated questions are actually relevant themes in the new branch of Dynamics called "linear dynamics". I'll try to briefly convey some of the basic aspects of this theory and then describe some recent developments.
