Geodesic
A Counterexample on Nontangential Convergence for Oscillatory Integrals
Publications de l'Institut Mathématique, _N_S_87 (2010) no. 101, p. 129

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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 $\varphi$.
Classification : 42B15 35B65 35J10
Keywords: Generalized time-dependent Schrödinger equation, nontangential convergence 
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     author = {Karoline Johansson},
     title = {A {Counterexample} on {Nontangential} {Convergence} for {Oscillatory} {Integrals}},
     journal = {Publications de l'Institut Math\'ematique},
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     year = {2010},
     language = {en},
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Karoline Johansson. A Counterexample on Nontangential Convergence for Oscillatory Integrals. Publications de l'Institut Mathématique, _N_S_87 (2010) no. 101, p. 129 . http://geodesic.mathdoc.fr/item/PIM_2010_N_S_87_101_a9/