- E29
[1SF] Let \(f:βββ\) be a \(C^ n\) class function , let \(πββ\) be a constant, and let \(g(x)= e^{π x}f(x)\). Show that, if \(p\) is a polynomial and \(q(x)=p(x+π)\), then
\[ p(D) g = e^{π x} [q(D) f] \quad . \]Note that we can also write the relation above as a βconjugationβ
\[ e^{-π x} \big[p(D) [ e^{π x} f ]\big] = p(D+π) f ~ . \]Solution 1
EDB β 1SF
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Authors:
"Mennucci , Andrea C. G."
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