Oleksienko M. Hardy classes generated by unitary representations of locally compact groups.

The thesis is devoted to an investigation of Hardy type spaces of complex analytic extensions of functions defined on irreducible orbits generated by infinite dimensional unitary representations of locally compact groups over a separable complex Hilbert space.Cauchy and Poisson type integral formulas for analytic functions defined on irreducible orbits generated by unitary representations of locally compact groups are established. Reduced Heisenberg group which is the fundamental concept in modern quantum field theory and its Schrodinger representation are investigated. The Cauchy type kernel for analytic extensions of functions defined on Gauss orbit under unitary Schrodinger representation of Heisenberg group is established. The theorem for radial boundary values of analytic extensions is proven. Thus the Hardy type space is defined.