知识与财富的链接
主要讨论局部域上的Gabor紧框架.首先,建立局部域上Gabor系{xm(bx)g(x-u(n)a)}m.n∈p构成L~2(K)上紧框架的特征.其次,给出Gabor系{X_m(bx)g(x-u(n)a)}_(m,n∈p)成为L~2(K)上标准正交基的充要条件.
This paper deals with Gabor tight frames on local fields. Firstly, the characterizations for the Gabor system $\{\chi_{m}(bx)g(x-u(n)a)\}_{m,n\in P}$ to be a tight frame in $L^{2}(K)$ are established. Sceondly, some necessary and sufficient conditions for the Gabor system $\{\chi_{m}(bx)g(x-u(n)a)\}_{m,n\in P}$ to be an orthonormal basis in $L^{2}(K)$ are presented.