Professor Anton Baranov Spoke at North British Functional Analysis Seminar in Newcastle, Great Britain

From October 9th – 10th, 2015, Anton Baranov, Professor at the Department of Applied Mathematics and Business Informatics, was a guest speaker at the North British Functional Analysis Seminar, which took place at Newcastle University in Great Britain. He shared his impressions of the event.

This seminar is one in a series that takes place two or three times a year in British universities. The participant universities include Oxford, Cambridge, Edinburgh University, and universities of Birmingham, Leeds, and Sheffield.

For each of the North British Seminars, two or three speakers are chosen, and each of them reads two one-hour lectures about their recent research. Leading specialists in operator theory from Europe (excluding Great Britain) and the U.S. are invited to the seminar. This year I was invited to talk about my research in spectral synthesis for linear operators and functional models. The second speaker was Prof. John McCarthy from Washington University, a renowned American mathematician. The series of papers that I was speaking about was implemented together with Dmitry Yakubovich from the Autonomous University of Madrid.

The general principle of the functional model is that an abstract linear operator in a Hilbertian space, which has certain additional characteristics, can be ‘modelled’ (built as a unitary equivalence) as a kind of relatively simple and specific operator in a definite space of analytic (or even integral) functions. In my work with Yakubovich, we demonstrated how one-dimensional perturbations of compact self-adjoining operators can be implemented as specific operators in Hilbertian spaces of integral functions, which were invented in 1960s by Louis de Branges, a brilliant American mathematician. After that, it turns out that it’s possible to find new and surprising characteristics of such perturbations.

Representatives of the Russian, and specifically St. Petersburg, school of functional analysis haven’t been invited to speak at this seminar for over ten years. That’s why it was especially nice to participate in this event and to speak on a topic specific for the St. Petersburg analytical school. Functional models and, in a broader sense, interactions between theory of functions and abstract theory of operators, have always been one of the key topics of research at this school. The school was founded by two of my teachers, Viktor Khavin, who unfortunately passed away recently, and Nikolay Nikolsky, who is today Professor at University of Bordeaux in France.