Generalized free time-dependent Schrödinger equation with initial data in Fourier Lebesgue spaces

Abstract

Consider the solution of the free time-dependent Schrödinger equation with initial data f. It is shown by Sjögren and Sjölin (1989) that there exists f in the Sobolev space H^s(R^d), s=d/2 such that tangential convergence can not be widened to convergence regions. In 2010 we obtained the corresponding results for a generalized version of the Schrödinger equation, where -Δ_x is replaced by an operator ϕ(D), with special conditions on ϕ. In this paper we show that similar results may be obtained for initial data in Fourier Lebesgue spaces.

Pre-version, 17 pages