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A note on analyticity properties of far field patterns
1. | Mathematisches Institut, Universität Leipzig, 04009 Leipzig, Germany |
2. | Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto |
3. | Aalto University, Department of Mathematics and Systems Analysis, FI-00076 Aalto, Finland |
References:
[1] |
F. E. Browder, Real analytic functions on product spaces and separate analyticity, Canad. J. Math., 13 (1961), 650-656.
doi: 10.4153/CJM-1961-054-1. |
[2] |
A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl., 16 (2008), 19-33.
doi: 10.1515/jiip.2008.002. |
[3] |
D. L. Colton and R. Kress, "Integral Equation Methods in Scattering Theory," John Wiley & Sons, New York, 1983. |
[4] |
D. L. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory," $2^{nd}$ edition, Springer-Verlag, Berlin, 1998. |
[5] |
F. Hartogs, Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen, insbesondere über die Darstellung derselben durch Reihen, welche nach Potenzen einer Veränderlichen fortschreiten, Math. Ann., 62 (1906), 1-88.
doi: 10.1007/BF01448415. |
[6] |
L. Hörmander, "An Introduction to Complex Analysis in Several Variables," $3^{rd}$ edition, North-Holland, Amsterdam, 1990. |
[7] |
N. Hyvönen, P. Piiroinen and O. Seiskari, Point measurements for a Neumann-to-Dirichlet map and the Calderón problem in the plane, SIAM J. Math. Anal., 44 (2012), 3526-3536.
doi: 10.1137/120872164. |
[8] |
A. Kirsch, The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media, Inverse Problems, 18 (2002), 1025-1040.
doi: 10.1088/0266-5611/18/4/306. |
[9] |
A. Kirsch, "An Introduction to the Mathematical Theory of Inverse Problems," $2^{nd}$ edition, Springer-Verlag, New York, 2011.
doi: 10.1007/978-1-4419-8474-6. |
[10] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems," Oxford University Press, Oxford, 2008. |
[11] |
S. G. Krantz, "Function Theory of Several Complex Variables," $2^{nd}$ edition, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1992. |
[12] |
J. L. Lions and E. Magenes, "Non-Homogeneous Boundary Value Problems and Applications," I, Springer-Verlag, New York, 1972. |
[13] |
A. I. Nachman, Reconstructions from boundary measurements, Ann. of Math., 128 (1988), 531-576.
doi: 10.2307/1971435. |
[14] |
R. G. Novikov, A multidimensional inverse spectral problem for the equation $-\Delta \psi + (v(x)-Eu(x))\psi=0$, translation in Funct. Anal. Appl., 22 (1988), 263-272.
doi: 10.1007/BF01077418. |
[15] |
A. G. Ramm, Recovery of the potential from fixed-energy scattering data, Inverse Problems, 4 (1988), 877-886.
doi: 10.1088/0266-5611/4/3/020. |
show all references
References:
[1] |
F. E. Browder, Real analytic functions on product spaces and separate analyticity, Canad. J. Math., 13 (1961), 650-656.
doi: 10.4153/CJM-1961-054-1. |
[2] |
A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl., 16 (2008), 19-33.
doi: 10.1515/jiip.2008.002. |
[3] |
D. L. Colton and R. Kress, "Integral Equation Methods in Scattering Theory," John Wiley & Sons, New York, 1983. |
[4] |
D. L. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory," $2^{nd}$ edition, Springer-Verlag, Berlin, 1998. |
[5] |
F. Hartogs, Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen, insbesondere über die Darstellung derselben durch Reihen, welche nach Potenzen einer Veränderlichen fortschreiten, Math. Ann., 62 (1906), 1-88.
doi: 10.1007/BF01448415. |
[6] |
L. Hörmander, "An Introduction to Complex Analysis in Several Variables," $3^{rd}$ edition, North-Holland, Amsterdam, 1990. |
[7] |
N. Hyvönen, P. Piiroinen and O. Seiskari, Point measurements for a Neumann-to-Dirichlet map and the Calderón problem in the plane, SIAM J. Math. Anal., 44 (2012), 3526-3536.
doi: 10.1137/120872164. |
[8] |
A. Kirsch, The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media, Inverse Problems, 18 (2002), 1025-1040.
doi: 10.1088/0266-5611/18/4/306. |
[9] |
A. Kirsch, "An Introduction to the Mathematical Theory of Inverse Problems," $2^{nd}$ edition, Springer-Verlag, New York, 2011.
doi: 10.1007/978-1-4419-8474-6. |
[10] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems," Oxford University Press, Oxford, 2008. |
[11] |
S. G. Krantz, "Function Theory of Several Complex Variables," $2^{nd}$ edition, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1992. |
[12] |
J. L. Lions and E. Magenes, "Non-Homogeneous Boundary Value Problems and Applications," I, Springer-Verlag, New York, 1972. |
[13] |
A. I. Nachman, Reconstructions from boundary measurements, Ann. of Math., 128 (1988), 531-576.
doi: 10.2307/1971435. |
[14] |
R. G. Novikov, A multidimensional inverse spectral problem for the equation $-\Delta \psi + (v(x)-Eu(x))\psi=0$, translation in Funct. Anal. Appl., 22 (1988), 263-272.
doi: 10.1007/BF01077418. |
[15] |
A. G. Ramm, Recovery of the potential from fixed-energy scattering data, Inverse Problems, 4 (1988), 877-886.
doi: 10.1088/0266-5611/4/3/020. |
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