Modulation space estimates for Schrödinger type equations with time-dependent potentials

Title:

Modulation space estimates for Schrödinger type equations with time-dependent potentials

Creator:

Wei, Wei

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5cc9dc84-de7d-4fe8-99f0-08a0e749c88e
uuid:5cc9dc84-de7d-4fe8-99f0-08a0e749c88e

Subject:

Schrödinger type equation, short-time Fourier transform, modulation space, classical Hamiltonian, and complex interpolation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

539-566

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:2

Harvested from:

CDK

Metadata only:

false