Geodesic
Uniqueness of the solution to inverse scattering problem with backscattering data
Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 97-111.

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Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(-\beta,\beta,k)$ $\forall\beta\in S^2$, $\forall k>0$, determine $q$ uniquely. 
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A. G. Ramm. Uniqueness of the solution to inverse scattering problem with backscattering data. Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 97-111. http://geodesic.mathdoc.fr/item/EMJ_2010_1_3_a5/

[1] B. Levin, Distribution of zeros of entire functions, AMS, Providence, RI, 1980 | MR | Zbl

[2] G. Polya, G. Szegő, Problems and theorems in analysis, problem III.6.5.322, v. 1, Springer Verlag, Berlin, 1983

[3] A. G. Ramm, “Uniqueness theorem for inverse scattering with non-overdetermined data”, J. Phys. A, 43 (2010), 112001 | DOI | MR | Zbl

[4] A. G. Ramm, “On the analytic continuation of the solution of the Schrödinger equation in the spectral parameter and the behavior of the solution to the nonstationary problem as $t\to\infty$”, Uspechi Mat. Nauk, 19 (1964), 192–194 (in Russian)

[5] A. G. Ramm, “Some theorems on analytic continuation of the Schrödinger operator resolvent kernel in the spectral parameter”, Izvestiya Acad. Nauk Armyan. SSR, Mathematics, 3 (1968), 443–464 (in Russian) | MR

[6] A. G. Ramm, “Recovery of the potential from fixed energy scattering data”, Inverse Problems, 4 (1988), 877–886 ; 5 (1989), 255 | DOI | MR | Zbl | DOI | MR | Zbl

[7] A. G. Ramm, “Stability estimates in inverse scattering”, Acta Appl. Math., 28:1 (1992), 1–42 | MR | Zbl

[8] A. G. Ramm, “Stability of the solution to inverse obstacle scattering problem”, J. Inverse and Ill-Posed Problems, 2:3 (1994), 269–275 | DOI | MR | Zbl

[9] A. G. Ramm, “Stability of solutions to inverse scattering problems with fixed-energy data”, Milan Journ of Math., 70 (2002), 97–161 | DOI | MR | Zbl

[10] A. G. Ramm, Inverse problems, Springer, New York, 2005 | MR

[11] A. G. Ramm, Scattering by obstacles, D. Reidel, Dordrecht, 1986 | MR | Zbl

[12] A. G. Ramm, A. I. Katsevich, The Radon transform and local tomography, CRC Press, Boca Raton, 1996 | MR | Zbl