Dissertation: Extension theory of operators in Krein and Pontryagin spaces and applications
The author has been able to improve a couple of classical theorems known in the area, namely Shmul’yan theorem on completion of nonnegative block operators and Krein famous theorem on description of selfadjoint contractive extensions of a Hermitian contraction. Using the key new results the author has proven various analogs for some other previously known results for not only wider classes of operators but also in the more general setting of Krein and Pontryagin spaces instead of a standard case of Hilbert spaces.
One of the approaches used in the dissertation is based on the notation of boundary triplets. In many cases, the modern boundary triplets’ methods have appeared to offer a more convenient tool than standard methods of extension theory, for instance, when treating boundary value problems or various spectral and scattering properties of differential operators.
“Extension theory of operators offers a general framework for investigating and solving various formally other types of problems appearing in the area of mathematical analysis and mathematical physics. In particular, the results in my PhD thesis have applications in the perturbation and spectral theory of operators, in scattering theory and they provide for instance a method to solve Hamburger type moment problems and Nevanlinna-Pick type interpolation problems”, says Dmytro Baidiuk who will defend his doctoral thesis at the University of Vaasa.
Dmytro Baidiuk, tel +358 404624563, email: dbaidiuk(at)uwasa.fi
Baidiuk, Dmytro (2016). Extension theory of operators in Krein and Pontryagin spaces and applications. Acta Wasaensia 354.
The public examination of M.Sc. Dmytro Baidiuk´s doctoral dissertation in the field of mathematics ”Extension theory of operators in Krein and Pontryagin spaces and applications” will be held on Monday, 22 August 2016 at 12 o’clock in Auditorium Kurten (Tervahovi) University of Vaasa.
Professor Jussi Behrndt (Technische Universität Graz) will act as an opponent and professor Seppo Hassi (University of Vaasa) as a custos. The examination will be held in English.