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

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A COUNTEREXAMPLE ON NONTANGENTIAL CONVERGENCE FOR OSCILLATORY INTEGRALS

Karoline Johansson

Department of Mathematics and Systems Engineering, Växjö University, Vejdes Plats 6,7, S-351 95 Växjö, Sweden

Abstract: Consider the solution of the time-dependent Schrödinger equation with initial data $f$. It is shown by Sjögren and Sjölin (1989) that there exists $f$ in the Sobolev space $H^s(\mathbf R^n)$, $s=n/2$ 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 time-dependent Schrödinger equation, nontangential convergence

Classification (MSC2000): 42B15; 35B65, 35J10

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