Analyticity properties and estimates of resolvent kernels near thresholds

M. Ben-Artzi*, Y. Dermenjian, J. C. Guillot

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

Resolvent estimates are derived for the family of ordinary differential operators (formula presented) It is assumed that c(y) = c± > 0, ρ(y) = p± for ±y > yc, and the kernels are studied in neighborhoods of the points {c 2±p2}, uniformly in compact intervals of p. This family arises in the direct integral decomposition of the acoustic propagator in layered media, -c2(y) ρ(y) ▽x,y (1/ρ(y) ▽x,y), x ∈ ℝn, and the Lemma A.2 For 0 ≤ arg z ≤ τ < π, s > 3/2, n ≥ 3, (A.10) ∥M(z)∥B(L2,s(Rn+1),L2,-s(Rn+1)) = O(1) as z → 0.

Original languageEnglish
Pages (from-to)1753-1770
Number of pages18
JournalCommunications in Partial Differential Equations
Volume25
Issue number9-10
DOIs
StatePublished - 2000

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