中文摘要：

研究有限维Hilbert空间上带有可逆结构的椭圆框架,给出了Gabor型可逆系统的刻画,并得到了Gabor型可逆系统椭圆框架向量的一些性质.特别地,给出了在Gabor型可逆系统下,一个框架向量何时具有椭圆对偶框架向量,以及如何在已有的Gabor椭圆框架基础上构造新的一族Gabor椭圆框架.

英文摘要：

This paper studies the ellipsoidal frames in finite dimensional Hilbert spaces , investigates the Oabor invertible systems and gets some properties of ellipsoidal frames. Especially, the paper gives the conditions of the existence of Parseval ellipsoidal frame vectors for a given frame vector and shows how to construct a new Gabor type ellipsoidal frames from two given Gabor frames.