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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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/
@article{PIM_2010_N_S_87_101_a9,
     author = {Karoline Johansson},
     title = {A {Counterexample} on {Nontangential} {Convergence} for {Oscillatory} {Integrals}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {129 },
     year = {2010},
     volume = {_N_S_87},
     number = {101},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2010_N_S_87_101_a9/}
}
TY  - JOUR
AU  - Karoline Johansson
TI  - A Counterexample on Nontangential Convergence for Oscillatory Integrals
JO  - Publications de l'Institut Mathématique
PY  - 2010
SP  - 129 
VL  - _N_S_87
IS  - 101
UR  - http://geodesic.mathdoc.fr/item/PIM_2010_N_S_87_101_a9/
LA  - en
ID  - PIM_2010_N_S_87_101_a9
ER  - 
%0 Journal Article
%A Karoline Johansson
%T A Counterexample on Nontangential Convergence for Oscillatory Integrals
%J Publications de l'Institut Mathématique
%D 2010
%P 129 
%V _N_S_87
%N 101
%U http://geodesic.mathdoc.fr/item/PIM_2010_N_S_87_101_a9/
%G en
%F PIM_2010_N_S_87_101_a9