1. Modulation space estimates for Schrödinger type equations with time-dependent potentials
- Creator:
- Wei, Wei
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Schrödinger type equation, short-time Fourier transform, modulation space, classical Hamiltonian, and complex interpolation
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public