0000000000855333
AUTHOR
Antonio Boccuto
A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
Abstract A Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces.
Integration of functions ranging in complex Riesz space and some applications in harmonic analysis
The theory of HenstockâKurzweil 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.