Generalized free time-dependent Schr\"odinger equation with initial data in Fourier Lebesgue spaces
Abstract
Consider the solution of the free time-dependent Schr\"odinger equation with initial data f. It is shown by Sj\"ogren and Sj\"olin (1989) that there exists f in the Sobolev space Hs(Rd), 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 Schr\"odinger equation, where -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.
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