Vasylyshyn T. Homomorphisms and ideals in algebras of differentiable functions on Banach spaces.

In the thesis it is investigated the spectrum (the set of maximal ideals) of a Wiener type algebra generated by -polynomials on Banach space and described derivations associated with elements of the spectrum. Also it is established an explicit formula for calculation of the radius-function on and described the spectrum of symmetric analytic functions of bounded type on the space of Lebesgue measurable essentially bounded functions on [0,1]. Some analogues of the polarization formula and polarization inequality for -polynomials on Banach space are obtained. A predual space of the space of -polynomials is constructed