Let f [epsilon] [S.sup.*.sub.S,[summation]] 2 (a, f) and g be the analytic extension of [f.sup.-1] to U.
Let f [epsilon] [l.sub.S,[summation]]([alpha], [phi]) and g be the analytic extension of [f.sup.-1] to U.
with supp u(t) [subset] [-B, B] x I, then by the Paley-Wiener Theorem we conclude that [??] has an analytic extension in C and there exists [kappa] > 0 such that for all t [member of] I, the function [??]([lambda]+i[sigma]) has the exponential order (1).
has an analytic extension in a neighborhood of the real axis.
Let [[lambda].sub.1] > 0 and [t.sub.0] [member of] I be fixed, and let [??](z) be the analytic extension of the Fourier transform of u(to)(x).
where [t.sub.0] [member of] [??](z) denotes the analytic extension of the Fourier transform of u([t.sub.0]) (x).
Then, from the Paley-Wiener Theorem we know that [??] has an analytic extension in C and there is [[kappa].sub.1] > 0 such that for t [member of] I,
Section 2 is devoted to the case when D(w; *) is non vanishing and has an analytic extension across [T.sub.1].
Taking into account (1.3) we see that the first identity in (1.4) can be regarded as an analytic extension of the weight w.
Whitney, "Analytic extensions
of differentiable functions defined in closed sets," Transactions of the American Mathematical Society, vol.
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