Asymptotic and approximate formulas in the inverse scattering problem for the Schrödinger operator

Saitō, Yoshimi

doi:10.1007/bfb0073051

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Y=d-r-'y=q(r-'y):=(qor)(y)1

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1989

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Cited by 2 publications

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“…For example, if (4) holds for all sufficiently large K > O then q ( x ) = q(1xl) if q belongs to the class of potentials for which the uniqueness of the solution of the inverse scattering problem is proved for the data A (W, 8 , K) given for all e', 8, E S 2 and all K sufficiently large. These are potentials q ( x ) for which /q(x)1 s c(1 + IxJ)-~, b > 3, c = constant > 0; see [6] (for an even larger class of potentials with b > l , see [9]). …”

Section: Y=d-r-'y=q(r-'y):=(qor)(y)mentioning

confidence: 99%

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Necessary and sufficient condition on the fixed-energy scattering data for the potential to be spherically symmetric

Ramm

Weaver

1989

Inverse Problems

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Section: Y=d-r-'y=q(r-'y):=(qor)(y)mentioning

confidence: 99%

“…given for all e', 8, E S 2 and all K sufficiently large. These are potentials q ( x ) for which /q(x)1 s c(1 + IxJ)-~, b > 3, c = constant > 0; see [6] (for an even larger class of potentials with b > l , see [9]).…”

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confidence: 99%