TY - JOUR
T1 - Analyticity properties and estimates of resolvent kernels near thresholds
AU - Ben-Artzi, M.
AU - Dermenjian, Y.
AU - Guillot, J. C.
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0034354518&partnerID=8YFLogxK
U2 - 10.1080/03605300008821566
DO - 10.1080/03605300008821566
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AN - SCOPUS:0034354518
SN - 0360-5302
VL - 25
SP - 1753
EP - 1770
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 9-10
ER -