Myronyuk M. Functional equations on locally compact Abelian groups

Object - functional equations on Abelian groups; objective - solution of some functional equations on locally compact Abelian groups in a class of normalized continuous positive defined functions; methods - Pontrjagin duality theory, structure theory for locally compact Abelian groups and algebraic theory of infinite Abelian groups; newness - the Bernstein equation was solved on an arbitrary subgroup of the group of rational numbers, it was obtained the description of automorphisms of the two dimensional integer-valued lattice for which all solutions of the Skitovich-Darmois equation are Gaussian, it was described compact totally disconnected Abelian groups and countable discrete periodic Abelian groups for which all not vanishing solutions of the Skitovich-Darmois equation are Gaussian, the Heyde equation was solved on a finite Abelian group; applications - the research is theoretical, results can be used in the theory of characterization problems on groups and in solving functional equation on groups.