Inst. of Mathematics

Division of Analysis
ul. Akademicka 2
15-267 Bialystok

Head of Division
Prof A. V. Lebedev
B. K. Kwasniewski


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Main interests:

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 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.

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