The head of “Functions Theory” department of IMM, doctor of sciences in mathematics Vugar Ismayilov has got an official invitation from Oxford University of England to give a talk at “Functional Analysis” workshop and carry out scientific discussion and was on a professional trip at Oxford University on 02.03.2017-18.03.2017.
The goal of the professional trip: Oxford University. Giving a talk at “Functional Analysis” workshop. Carrying out scientific discussions with prof. Charles Batty and other research workers of Oxford University, participation at different seminars. Doctor of sciences in mathematics Vugar Ismayilov gave an one hour talk “Representation of as a sum of its subalgebras and some applications”. The talk was devoted to representation of a space of continuous functions determined in compact Hausedorff space in the sum of its subalgebras.
Note that this problem is in the center of attention of English mathematicians.
In 1992, the English scientists Sproston and Strauss have found a necessary condition for the representation and the appropriate result was published in “Journal of London Mathematical Society”. The same result was obtained for compact metric spaces by Sternfield. The result obtained by Vugar Ismayilov contains the necessary condition for the above mentioned representation problem. If the sum of algebras consists of two addends, then the obtained necessary condition is a sufficient condition as well and it is equipotent with Sproston-Strauss’s result. The advantage of the new result, its geometrical description was explained to the participants, and some problems in this direction were remarked. The main problem is to find necessary and sufficient conditions for the sum of arbitrary number algebras.
During this professional trip, discussions with prof. C.Batty and D.Seifert and other members of functional analysis group were carried out. During discussions, the methods for studying density and completeness conditions of the sum of algebras in function pace and application it to representation problem were looked for. At the same time, suggestions for weakening the Sternfield condition for obtaining a necessary condition were made.
Vugar Ismayilov has participated at other seminars of Oxford Universityt as well.
For brief content of the talk see: (see: https://www.maths.ox.ac.uk/node/24710).

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