Functions of several Cayley-Dickson variables and manifolds over them

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are proved in the new generalized form for functions of Cayley-Dickson variables instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated

Quasi-invariant measures on a group of diffeomorphisms of an infinite-dimensional real manifold and induced irreducible unitary representations

Quasi-invariant strongly differentiable measures on a group of diffeomorphisms of an infinite-dimension al real Banach manifold, relative to dense subgroups, are constructed. These measures are used for the investigation of irreducible unitary representations