Publications de l'Institut Mathématique, Nouvelle Série Vol. 87(101), pp. 129–137 (2010) 

A COUNTEREXAMPLE ON NONTANGENTIAL CONVERGENCE FOR OSCILLATORY INTEGRALSKaroline JohanssonDepartment of Mathematics and Systems Engineering, Växjö University, Vejdes Plats 6,7, S351 95 Växjö, SwedenAbstract: Consider the solution of the timedependent Schrödinger equation with initial data $f$. It is shown by Sjögren and Sjölin (1989) that there exists $f$ in the Sobolev space $H^s(\mathbf R^n)$, $s=n/2$ such that tangential convergence can not be widened to convergence regions. In this paper we show that the corresponding result holds when $\Delta_x$ is replaced by an operator $\varphi(D)$, with special conditions on $\varphi$. Keywords: Generalized timedependent Schrödinger equation, nontangential convergence Classification (MSC2000): 42B15; 35B65, 35J10 Full text of the article: (for faster download, first choose a mirror)
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