7 research outputs found
Asymptotic Hyperfunctions, Tempered Hyperfunctions, and Asymptotic Expansions
We introduce new subclasses of Fourier hyperfunctions of mixed type,
satisfying polynomial growth conditions at infinity, and develop their sheaf
and duality theory. We use Fourier transformation and duality to examine
relations of these 'asymptotic' and 'tempered' hyperfunctions to known classes
of test functions and distributions, especially the Gelfand-Shilov-Spaces.
Further it is shown that the asymptotic hyperfunctions, which decay faster than
any negative power, are precisely the class that allow asymptotic expansions at
infinity. These asymptotic expansions are carried over to the
higher-dimensional case by applying the Radon transformation for
hyperfunctions.Comment: 31 pages, 1 figure, typos corrected, references adde
Structural theorems for quasiasymptotics of ultradistributions
We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the origin of ultradistributions and discuss connections with Gelfand-Shilov type spaces
Asymptotic boundedness and moment asymptotic expansion in ultradistribution spaces
We obtain structural theorems for the so-called S-asymptotic and quasiasymptotic boundedness of ultradistributions. Using these results, we then analyze the moment asymptotic expansion (MAE), providing a full characterization of those ultradistributions satisfying this asymptotic formula in the one-dimensional case. We also introduce and study a uniform variant of the MAE
Mathematics of the Quantum Zeno Effect
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