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 folowing 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
- 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.