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Seeing the Invisible and Maxwell’s Equations

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Quaternion and Clifford Fourier Transforms and Wavelets

Part of the book series: Trends in Mathematics ((TM))

Abstract

In this chapter we study inverse scattering for Dirac operators with scalar, vector and quaternionic potentials. For that we consider factorizations of the Helmholtz equation and related fundamental solutions; the standard Green’s function and Faddeev’s Green function. This chapter is motivated by optical coherence tomography.

Mathematics Subject Classification (2010). Primary 30G35; secondary 45B05.

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Authors and Affiliations

  1. Institute of Applied Analysis, TU Bergakademie Freiberg, Prüferstr. 9, D-09596, Freiberg, Germany

    Swanhild Bernstein

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  1. Swanhild Bernstein
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Correspondence to Swanhild Bernstein .

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Editors and Affiliations

  1. , Department of Material Science, International Christian University, Osawa 3-10-2Mitaka-shi, Tokyo, 181-8585, Japan

    Eckhard Hitzer

  2. School of Computer Science and, Electronic Engineering, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom

    Stephen J. Sangwine

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Bernstein, S. (2013). Seeing the Invisible and Maxwell’s Equations. In: Hitzer, E., Sangwine, S. (eds) Quaternion and Clifford Fourier Transforms and Wavelets. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0603-9_13

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