Local two-radii theorem in symmetric spaces

Various classes of functions on a non-compact rank-one Riemannian symmetric space $X$ with vanishing integrals over all balls of fixed radius are studied. A description in the form of a series in hypergeometric functions is obtained for such classes and a uniqueness theorem is proved. This makes it possible to establish the local two-radii theorem in $X$ in a definitive form.
Bibliography: 45 titles.