10 research outputs found
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 -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 non-Archimedean groups and semigroups of loops and paths, their representations
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