Ellipsoidal Frames For Finite Dimensional Hilbert Spaces

This paper studies the ellipsoidal frames in finite dimensional Hilbert spaces. We study dualframes and give the conditions for the existence of the dual ellipsoidal Parseval frames.. Then weshow when the sum of two ellipsoidal frames is still a frame. We study ellipsoidal frames withinvertible structure in finite dimensional Hilbert spaces, investigate the invertible systems and getsome properties of ellipsoidal frames. Especially, we focus on the invertible systems generated by oneor two invertible operators. At last we present the Gabor type invertible systems and obtain someproperties of ellipsoidal frame vectors and show how to construct a new Gabor type ellipsoidal framesfrom two given Gabor frames.