Weekly seminar on 26 th of April 2017, 10:00 a.m. will feature 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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