Integration of Functions Ranging in Complex Riesz Space and Some Applications in Harmonic Analysis

The theory of Henstock–Kurzweil integral is generalized to the case of functions ranging in complex Riesz space $R$ and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the $R$-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.