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References
S. Bergman, Integral Operators in the Theory of Linear Partial Differential Equations, Springer-Verlag, Berlin, 1969.
R.P. Boas, Entire Functions, Academic Press, New York, 1954.
D. Colton, Partial Differential Equations in the Complex Domain, Pitman Press, London, 1976.
D.Colton, The Solution of Boundary Value Problems by the Method of Integral Operators, Pitman Press, London, to appear.
D. Colton, On the inverse scattering problem for axially symmetric solutions of the Helmholtz equation, Quart.J.Math.22 (1971), 125–130.
D.Colton, The inverse scattering problem for acoustic waves in a spherically stratified medium, Proc.Edin.Math.Soc., to appear.
D.Colton, A reflection principle for solutions to the Helmholtz equation and an application to the inverse scattering problem, Glasgow Math.J. to appear.
D.Colton and W.Wendland, Constructive methods for solving the exterior Neumann problem for the reduced wave equation in a spherically symmetric medium, Proc.Roy.Soc.Edin., to appear.
R.P. Gilbert, Function Theoretic Methods in Partial Differential Equations, Academic Press, New York, 1969.
R.P. Gilbert, Constructive Methods for Elliptic Equations, Springer-Verlag Lecture Note Series Vol. 365, Berlin, 1974.
P. Hartman and C. Wilcox, On solutions of the Helmholtz equation in exterior domains, Math.Zeit. 75 (1961), 228–255.
S.N. Karp, Far field amplitudes and inverse diffraction theory, in Electromagnetic Waves, R.E. Langer, editor, University of Wisconsin Press, Madison, 1962, 291–300.
M.M. Lavrentiev, Some Improperly Posed Problems of Mathematical Physics, Springer-Verlag, Berlin, 1967.
P.D. Lax and R.S. Phillips, Scattering Theory, Academic Press, New York, 1967.
R.F. Millar, Singularities of two-dimensional exterior solutions of the Helmholtz equation, Proc.Camb.Phil.Soc. 69 (1971), 175–188.
R.F.Millar, Singularities of solutions to exterior analytic boundary value problems for the Helmholtz equation in three independent variables I. The plane boundary, SIAM J.Math.Anal., to appear.
C. Müller, Radiation patterns and radiation fields, J.Rat.Mech.Anal. 4 (1955), 235–246.
L.E. Payne, Improperly Posed Problems in Partial Differential Equations, SIAM Publications, Philadelphia, 1975.
C. Rorres, Low energy scattering by an inhomogeneous medium and by a potential, Arch.Rat.Mech.Anal. 39 (1970), 340–357.
B.D. Sleeman, The three-dimensional inverse scattering problem for the Helmholtz equation, Proc.Camb.Phil.Soc. 73 (1973), 477–488.
I.N. Vekua, New Methods for Solving Elliptic Equations, John Wiley, New York, 1967.
V.H. Weston, J.J. Bowman and E. Ar, On the inverse electromagnetic scattering problem, Arch.Rat.Mech.Anal. 31 (1968), 199–213.
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Colton, D. (1976). Integral operators and inverse problems in scattering theory. In: Meister, V.E., Wendland, W.L., Weck, N. (eds) Function Theoretic Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087622
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DOI: https://doi.org/10.1007/BFb0087622
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