Date of Award

May 2016

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Lijing Sun

Committee Members

Dashan Fan, Gabriella Pinter, Lei Wang, Chao Zhu


Alpha-Modulation Space, Asymptotic Estimates, Dispersive Equations


The alpha-modulation space is a function space developed by Grobner in 1992. The alpha-modulation space is a generalization of the modulation space and Besov space. In this thesis we obtain asymptotic estimates for the Cauchy Problem for dispersive equation, a generalized half Klein-Gordon, and the Klein-Gordon equations. The wave equations will also be considered in this thesis too. These estimates were found by using standard tools from harmonic analysis. Then we use these estimates with a multiplication algebra property of the alpha-modulation space to prove that there are unique solutions locally in time for a nonlinear version of these partial differential equations in the function space of continuous function in time and alpha-modulation in the spatial component. These results are obtained by using the fixed point theorem.

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Mathematics Commons