Mytrofanov M. Continuous mapping on Banach spaces. Approximations and relations to algebras of analytic functions

The thesis is devoted to investigation of the problem of approximation of continuous mappings on Banach and Frйchet spaces by analytic mappings for real spaces and *-analytic mappings for complex spaces. Also, *-analytic mappings on complex spaces are investigated in the thesis and applied in infinite dimensional complex analysis. The following results are obtained in the thesis: it is established conditions of approximation of continuous maps by *-analytic mappings on separable Banach and Frйchet spaces; an analogue of the Wiener theorem for infinite dimensional spaces is proved; Hardy-type Hilbert spaces of analytic and *-analytic functions on a polydisk of the Hilbert space are investigated; some applications of *-polynomials for construction and investigation of complex generalized functions are proposed.