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Generalized gaussian bounds for discrete convolution powers

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Figure

Figure 1: Illustration of the contour used in the case − η 2 ≤ ρ  ζ
Figure 2: Illustration for the explicit (left) and implicit (right) cases of the different domains in the (j, n) plane where generalized Gaussian estimates are obtained; here K = 3 with α 1 < 0 and α 2 6= α 3 > 0.
Figure 3: Left: typical contour used when (j, n) ∈ D 3 in the case depicted in Figure 2 where all α k are distinct α 1 < α 2 < α 3 (case A)
Figure 4: Illustration of the contour Γ e k used in the proof of Lemma 11 and Lemma 12.
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