加权空间L_W^2(R^d)上的向量Gabor框架

Vector Gabor Frames on Weighted Lebesgue SpaceL_W^2 (R^d)

讨论加权空间L_W^2(Rd)上的Gabor框架,得到该空间具有向量Gabor框架的一个必要条件,即权函数W(x)满足0<A≤W(x)≤B<+∞,a.e.,A、B为常数。进而说明加权空间L2W(Rd)与空间L2(Rd)本质上一样,从而L2W(Rd)上不存在Gabor框架,除非权函数W(t)是本质有界的。

Discussing Gabor frames on space L2W(T5Rd),we get essential condition of weight function W(x) when there exists Gabor frame on L2W(Rd),the weight function W(x) satisfies:0<A≤W(S)≤B<+∞,a.e.where A and B are two constants.We further show that the space L2(Rd) is essentially as the same as L2W(Rd).Thereby,three doesn′t exist any Gabor frame on weighted space L2W(Rd) unless the weight function W(x) is essential bounded.