 1257 Asao Arai
 Asymptotic Analysis of the Fourier Transform of a Probability Measure
with Application to Quantum Zeno Effect
(131K, Latex 2e)
May 15, 12

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Abstract. Let $\mu$ be a probability measure on the set $\BBR$ of real numbers
and $\hat \mu(t):=\int_{\BBR}e^{it\lambda}d\mu(\lambda)$ ($t\in \BBR$) be the Fourier transform
of $\mu$ ($i$ is the imaginary unit). Then, under suitable conditions,
asymptotic formulae of $\hat \mu(t/x)^{2x}$ in $1/x$ as $x o \infty$ are derived.
These results are applied to the socalled quantum Zeno effect to establish asymptotic formulae
of its occurrence probability in the inverse of the number $N$ of measurements
made in a time interval as $N o\infty$.
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