ScalingStacks

Lemma 4.6 . [03HB]

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Lemma 4.6.

The following uniform estimates hold for all j∈ℤ+j\in\mathbb{Z}_{+} and h≥0h\geq 0,

(4.53) ℱ⁡(z)≤(1+π)​e−j​z22+F​(t0​(z)),\mathcal{F}(z)\leq(1+\sqrt{\pi})e^{-\frac{jz^{2}}{2}+F(t_{0}(z))},
(4.54) 𝒰⁡(z)≤(1+π)​e−j​z22+U​(s0​(z)).\mathcal{U}(z)\leq(1+\sqrt{\pi})e^{-\frac{jz^{2}}{2}+U(s_{0}(z))}.

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