Weekly seminar on June 04, 2014, 10.00 a.m. will feature a report  by  Miqdad  Imdad oglu Ismailov, senior research worker of the Department of  Non-Harmonic Analysis, entitled  “On a generalization of frame and stability of it”.

Recently, from a practical point of view, the interest in frames greatly increased. Recall that the frames were introduced Duffin and Schaeffer in1952 to study the deep problems of nonharmonic analysis. A lot of work of  P. Casazza, O. Christensen, R. Balan, A. Aldrobi and others were devoted to frames.  G . Gröchenig extended the  concepts of frame for Banach spaces and introduced the notion of atomic decomposition and Banach frame. There are generalizations of the frame in Hilbert and Banach spaces, such as g-frames , x_d-frames ,g -Banach frames. An important issue is the stability study of frames and frame recovery formula.

Our aim is to study analogues of known results concerning Banach space of vector valued  sequences. In this work it is introduced the  concepts of  x- frame, b – atomic decomposition, the stability results of  results g-frames , x- frames and  b-atomic decomposition as well as recovery formula over   x-frame were obtained.