Kalyuzhnyi A. Classic and quantum hypergroups.

The dissertation is devoted to the theory of classic and quantum hypergroups. A main theorems of harmonic analysis on locally compact groups transferred to the locally compact hypergroups. The spectral theory of orthogonal polynomials in several variables is established. It is described an infinitesimal objects for hypergroups coming from Lie groups via the construction of unital orbital morphisms. The Lie theory is transferred to the one-dimensional hypergroups. It is proposed a method of construction of quantum hypergroups by conditional expectations on quantum groups, and it is constructed several series of new examples of nontrivial quantum hypergroups. For matched pair of Lie groups it is obtained a formulae for a pair of cocicles on Lie groups by a pair of cocicles of the corresponding matched pair of Lie algebras and it is constructed a new examples of locally compact quantum groups.