ScalingStacks

Lemma 4.8 . [03HF]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Lemma 4.8.

There is an absolute constant C0>0C_{0}>0 independent of j∈ℤ+j\in\mathbb{Z}_{+} and h≥0h\geq 0 such that the following uniform estimate holds for all z≥1z\geq 1,

(4.79) 0<eF^​(z)+U^​(z)𝒲⁡(z)≤C0,0<\frac{e^{\widehat{F}(z)+\widehat{U}(z)}}{\mathcal{W}(z)}\leq C_{0},

where

(4.80) F^​(z)=−j​z22+F⁡(t0​(z))\widehat{F}(z)=-\frac{jz^{2}}{2}+F(t_{0}(z))

and

(4.81) U^​(z)=−j​z22+U⁡(s0​(z)).\widehat{U}(z)=-\frac{jz^{2}}{2}+U(s_{0}(z)).

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.