Inverse Scattering for the 1-D Helmholtz Equation

被引：0

作者：

Beltita, Ingrid ^{[1
]}

Bunoiu, Renata ^{[2
]}

机构：

[1] Romanian Acad, Inst Math Simion Stoilow, POB 1-764, Bucharest, Romania

[2] CNRS, IECL, UMR 7502, F-57045 Metz, France

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2016年 / 10卷 / 04期

关键词：

LINE;

D O I：

10.1007/s11785-014-0441-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a uniqueness result for Nevanlinna functions. and this result is then used to give an elementary proof of the uniqueness in the inverse scattering problem for the equation on . Here is a real positive measurable function that is bounded from below by a positive constant, and is close to at +/- infinity.

引用

页码：639 / 666

页数：28

共 13 条

[1]

Aktosun T., 1990, INTEGRAL EQU OPER TH, V30, P279

[2]

Aronszajn N., 1956, J. Anal. Math, V5, P321

[3] Inverse scattering in a layered medium [J].

Beltita, I .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (9-10) :1739-1786

[4] Scattering and inverse scattering for a left-definite Sturm-Liouville problem [J].

Bennewitz, C. ;

Brown, B. M. ;

Weikard, R. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (08) :2380-2419

[5] Time and frequency domain scattering for the one-dimensional wave equation [J].

Browning, BL .

INVERSE PROBLEMS, 2000, 16 (05) :1377-1403

[6]

BROWNING BL, 1999, THESIS U WASHINGTON

[7] ON THE INVERSE SCATTERING PROBLEM FOR THE HELMHOLTZ-EQUATION IN ONE DIMENSION [J].

CHEN, Y ;

ROKHLIN, V .

INVERSE PROBLEMS, 1992, 8 (03) :365-391

[8] INVERSE SCATTERING ON THE LINE [J].

DEIFT, P ;

TRUBOWITZ, E .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1979, 32 (02) :121-251

[9]

Faddeev L.D., 1959, USP MAT NAUK, V14, P72

[10] OPERATOR METHODS FOR INVERSE SCATTERING ON THE REAL LINE [J].

MELIN, A .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1985, 10 (07) :677-766

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