Today, at the institute seminar was featured a report by  head of the Department of the “Non-harmonic Analysis” of the Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, Corresponding Member of ANAS,  Professor Bilal Bilalov  entitled by “Some problems of atomic dec omposition and frames. t-frames.  The concept of  uncountable frames  in non-separable hilbert spaces”.

In report  the  frames in Hilbert and Banach spaces are considered and under a Noetherian mapping their properties are studied. An  atomic decompositions in Banach spaces is also considered. The concept of K–closeness is introduced. The stability of the frame properties and atomic decompositions  with respect to  K–closeness  are proved. The concept of a t-frame associated with a Hilbert tensor product is introduced.  All the properties of ordinary frames are transferred  to this case. The Noetherian perturbation of  t-frames is considered. The stability of the t-frameness with respect to quadratic closeness  is proved. The concepts of Bessel  systems  and frames in non-separable Hilbert spaces are introduced. Many results related to usual frames are extended to new case.

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