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.
"The Union Problem and The Category Problem of Sets of Uniqueness in the Theory of Orthogonal Series." Real Anal. Exchange 44 (1) 65 - 76, 2019. https://doi.org/10.14321/realanalexch.44.1.0065