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math.AP2019
Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed
Sophia Bugarija, Peter C. Gibson, Guanghui Hu +2
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitraril…
math.AP2016
Fourier expansion of disk automorphisms via scattering in layered media
Peter C. Gibson
A family of orthogonal polynomials on the disk (which we call scattering polynomials) serves to formulate a remarkable Fourier expansion of the composition of a sequence of Poincar…