Geodesic
Oscillatory Integrals with Nonhomogeneous Phase Functions Related to Schrödinger Equations
Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 306-317

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In this paper we consider solutions to the free Schrödinger equation in $n+1$ dimensions. When we restrict the last variable to be a smooth function of the first $n$ variables we find that the solution, so restricted, is locally in ${{L}^{2}}$ , when the initial data is in an appropriate Sobolev space.
DOI : 10.4153/CMB-1998-043-1
Mots-clés : 42A25, 42B25 
Kolasa, Lawrence A. Oscillatory Integrals with Nonhomogeneous Phase Functions Related to Schrödinger Equations. Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 306-317. doi: 10.4153/CMB-1998-043-1
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     author = {Kolasa, Lawrence A.},
     title = {Oscillatory {Integrals} with {Nonhomogeneous} {Phase} {Functions} {Related} to {Schr\"odinger} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {306--317},
     year = {1998},
     volume = {41},
     number = {3},
     doi = {10.4153/CMB-1998-043-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-043-1/}
}
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