The scientific seminar of the S. M. Nikolskii Mathematical Institute on differential and functional differential equations under the guidance of Professor A.L. Skubachevskii

November 13, 2018, at 12:00 in the auditorium 398 the scientific seminar of the S. M. Nikolskii Mathematical Institute on differential and functional differential equations under the guidance of Professor A.L. Skubachevskii.

Speaker: Bakhtigareeva Elza, Ph.D., S. M. Nikolskii Mathematical Institute.

Topic: Method of non-degenerate operators for constructing optimal envelopes.

The talk is devoted to the construction of optimal embeddings for a given cone of non-negative measurable functions with monotonicity properties. Construction of optimal embeddings for a given cone of non-negative measurable functions, estimates of positive operators on them has important applications in various areas of analysis, such as, for example, the theory of function spaces, approximation theory, the theory of embeddings, interpolation theory.

The general method of construction of optimal envelopes by means of including into quasi-norm specially picked up non- degenerate operators is developed. The constructions of operators with such properties depend essentially on concrete variants of quasi-norms and on different monotonicity conditions.  The concretizations of the general results in cases of constructing optimal ideal envelopes for the cone of nonnegative decreasing functions and for the cone of nonnegative doubly monotone functions will be presented.