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arXiv · 1102.2998

Generalized free time-dependent Schr\"odinger equation with initial data in Fourier Lebesgue spaces

Karoline Johansson
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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 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 Schr\"odinger equation, where -\Delta_x is replaced by an operator \phi(D), with special conditions on \phi. In this paper we show that similar results may be obtained for initial data in Fourier Lebesgue spaces.

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Karoline Johansson. 2011-02-15. Generalized free time-dependent Schr\"odinger equation with initial data in Fourier Lebesgue spaces. https://arxiv.org/abs/1102.2998

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