The Union Problem and The Category Problem of Sets of Uniqueness in the Theory of Orthogonal Series

Abstract

These problems are considered for a wide range of orthogonal series. That is to say for trigonometric, Walsh, and other series on systems of characters of zero-dimensional compact abelian groups with the second axiom of countability. By this the sets of uniqueness are regarded for one-dimensional and multiple orthogonal series for many types of convergence.