## Abstract We consider the wholeβline inverse scattering problem for SturmβLiouville equations which have constant coefficients on a halfβline. Since in this case the reflection coefficient determines a WeylβTitchmarsh __m__βfunction, it determines the coefficients up to some simple Liouville tran
Uniqueness result for inverse problem of geophysics II
β Scribed by A.G. Ramm; G.Q. Xie
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 205 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0893-9659
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π SIMILAR VOLUMES
Let VZu+k2u+k2a~(z)u+V.(a~(~)Vu) = -6(cc-y) inR3, where al(z) EL'(D), a&) E H'(D), D E R3\_ = {z : 13 < 0) is a finite region, aj(Z) = 0 outside of D, j = 1,2, 1 + 02 > 0, al = El. Assume that thedatau(l,y,k),V~,yEP={I:13=0}8ndallkE(O,ko),ko>O is an arbitrary small number, are given. THEOREM. The ab
Let[V2 + k2n(x~,23)]u(x1,x2,x3) = -6(x1 -y1)6(x2 -y2)6(~3 -ys) in R"+. Assume that U(XI,X~,X~ = 0, yl,y2 = 0, y3 = 0, k) is measured at the plane P := {x : 23 = 0) for all positions of the source on the line y = (yi, y2 = 0, ys = 0), -oo < yr < 00, and receiver on the plane (~1, x2, x3 = 0), -oo < x