Abstract:
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.
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