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Summary: Sets of uniqueness of the power of the continuum
J. Marshall Ash and Gang Wang
Abstract. By means of the axiom of choice, the authors show that there exist
sets of the power of the continuum that are sets of uniqueness for spherical
convergence and sets of uniqueness for spherical Abel summability.
Consider the multiple trigonometric series
S (x) =
nZd
cneinx
,
where n = (n1, ..., nd) , x = (x1, ..., xd) Td
= [-, )
d
and nx denotes the scaler
product of n and x, n1x1 + ... + ndxd. Say that S (x) converges spherically to the
complex number s at x if
lim
R
SR (x) = lim
R
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