Laboratory of Functional Analysis

1. dr hab. Bartosz Kwaśniewski
2. dr Justyna Makowska
3. dr Andrew McKee
4. dr Krzysztof Zajkowski
5. mgr Krzysztof Bardadyn

The research of the division is related to all the branches of modern analysis that are concentrated around the theory of non-local (especially weighted shifts) or singular operators and equations associated to them. The following issues are within the wide scope of our interests:

• operator algebras associated to authomorphisms and endomorphisms
• topological and dynamical methods of calculating spectral characteristics of non-local operators
• ergodic theory and entropy
• structure of operator algebras generated by the symbolic calculus of pseudo-differential and non-local operators
• Perturbation theory for non-local operators
• non-local functional equations and differential operators with delta-potential
• extensions of symmetric operators to self-adjoint ones.

The methods and results that we investigate and use in the theory of functional equations generated by non-local or singular operators have also application in stochastic analysis, dynamical systems, pseudo-differential operators and convolution operators with oscillating coefficients, and also in the theory of equations with small parameter and resonances, thermodynamics and stochastic physics. All of the members of the division take part in the scientific project entitled: Operator algebras generated by dynamical systems: spectral, asymptotic and entropic characteristics granted by the Polish Minister of Science and Higher Education
Grant no: N N201 382634
Head of the project: Prof. A. B. Antonevich