We present an overview of the mathematics underlying the quantum Zeno effect.
Classical, functional analytic results are put into perspective and compared
with more recent ones. This yields some new insights into mathematical
preconditions entailing the Zeno paradox, in particular a simplified proof of
Misra's and Sudarshan's theorem. We empahsise the complex-analytic structures
associated to the issue of existence of the Zeno dynamics. On grounds of the
assembled material, we reason about possible future mathematical developments
pertaining to the Zeno paradox and its counterpart, the anti-Zeno paradox, both
of which seem to be close to complete characterisations.Comment: 32 pages, 1 figure, AMSLaTeX. In: Mathematical Physics Research at
the Leading Edge, Charles V. Benton ed. Nova Science Publishers, Hauppauge
NY, pp. 111-141, ISBN 1-59033-905-3, 2003; revision contains corrections from
the published corrigenda to Reference [64
