Abstract
There is a deep connection between the theory of several complex variables and complex Clifford analysis. We will use a Borel—Pompeiu formula in ℂn and the representation of holomorphic functions obtained in the context of Clifford analysis to study the inverse scattering problem for an n-dimensional Schròdinger-type equation. Equations are found for reconstructing the potential from scattering data purely by quadratures. The solution also helps elucidate the problem of characterizing admissible scattering data. Especially we do not need a “miraculous condition”.
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Bernstein, S. (2004). Multidimensional Inverse Scattering Associated with the Schròdinger Equation. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_2
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DOI: https://doi.org/10.1007/978-1-4612-2044-2_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3525-1
Online ISBN: 978-1-4612-2044-2
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