Lemma 5.11 . [0547] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Lemma 5.11 .
Let
(5.148)
F ^ ( z ) \displaystyle\widehat{F}(z)
≡ − j z n 2 + F ( t 0 ( z ) ) , \displaystyle\equiv-\frac{jz^{n}}{2}+F(t_{0}(z)),
(5.149)
G ^ ( z ) \displaystyle\widehat{G}(z)
≡ − j z n 2 + G ( u 0 ( z ) ) , \displaystyle\equiv-\frac{jz^{n}}{2}+G(u_{0}(z)),
then for all η ≥ 0 \eta\geq 0 , when z ≥ η 2 n z\geq\eta^{\frac{2}{n}} ,
F ^ ( z ) + η ⋅ z n 2 \widehat{F}(z)+\eta\cdot z^{\frac{n}{2}} is decreasing and G ^ ( z ) − η ⋅ z n 2 \widehat{G}(z)-\eta\cdot z^{\frac{n}{2}} is increasing.