Geodesic
Modulation space estimates for Schrödinger type equations with time-dependent potentials
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 539-566 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We give a new representation of solutions to a class of time-dependent Schrödinger type equations via the short-time Fourier transform and the method of characteristics. Moreover, we also establish some novel estimates for oscillatory integrals which are associated with the fractional power of negative Laplacian $(-\Delta )^{\kappa /2}$ with $1\leq \kappa \leq 2$. Consequently the classical Hamiltonian corresponding to the previous Schrödinger type equations is studied. As applications, a series of new boundedness results for the corresponding propagator are obtained in the framework of modulation spaces. The main results of the present article include the case of wave equations.
We give a new representation of solutions to a class of time-dependent Schrödinger type equations via the short-time Fourier transform and the method of characteristics. Moreover, we also establish some novel estimates for oscillatory integrals which are associated with the fractional power of negative Laplacian $(-\Delta )^{\kappa /2}$ with $1\leq \kappa \leq 2$. Consequently the classical Hamiltonian corresponding to the previous Schrödinger type equations is studied. As applications, a series of new boundedness results for the corresponding propagator are obtained in the framework of modulation spaces. The main results of the present article include the case of wave equations.
DOI : 10.1007/s10587-014-0118-5
Classification : 35Q40, 35Q41, 35R11, 42B35
Keywords: Schrödinger type equation; short-time Fourier transform; modulation space; classical Hamiltonian; complex interpolation 
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     author = {Wei, Wei},
     title = {Modulation space estimates for {Schr\"odinger} type equations with time-dependent potentials},
     journal = {Czechoslovak Mathematical Journal},
     pages = {539--566},
     year = {2014},
     volume = {64},
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     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0118-5/}
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Wei, Wei. Modulation space estimates for Schrödinger type equations with time-dependent potentials. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 539-566. doi: 10.1007/s10587-014-0118-5

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