Preprints and Lectures

My Publications

My Papers(pdf) -- in reverse chronological order

Some Preprints and Lectures by Topic

Estimates for Scattering

An Estimate for the Free Helmholtz Equation that Scales. -- The Helmholtz equation in R^n scales simply with dilations and commutes with translations. We introduce some norms which have the same properties, and with which we can prove estimates that depend sharply on wavenumber.

Transmission Eigenvalues

Transmission Eigenvalues: some degenerate and singular cases --- jointly written with Valery Serov proves existence of transmission eigenvalues for positive contrasts approaching zero or infinity at the boundary. Also gives an elementary lower bound for the counting function.
Discreteness of TE's and UTC's Talk (at Newton Institute Workshop) about the paper below.
Discreteness of TE's and UTC's proves the discreteness of transmission eigenvalues assuming only coercivity of the contrast on the boundary of the domain.
AIP 2007 Lecture on existence of TE's
Existence of Transmission Eignevalues (joint paper with Lassi Paivarinta)
Survey of the interior transmission problem and non-existence of TE's in the Born approximation. (joint paper with David Colton and Lassi Paivarinta)

The Scattering Support (the support of a far field)

Delaware Summer School Lectures on the inverse source problem and far field support. Read with caution; some parts still need a little revision.
AIP2005 Lecture on the Inverse Source Problem and the support of a far field.
Some Transparencies outlining the main practiclal aspects of the scattering support.
Some more Transparencies outlining more theoretical aspects of the scattering support.
The Scattering Support This paper (joint work with Steve Kusiak) introduces the convex scattering support of a far field and describes the theoretical basis for computing it.
A Range Test ... This paper (joint work with Roland Potthast and Steve Kusiak) implements a numerical test for finding the scattering support for the inverse scattering problem.
The Scattering Support in a Non-Uniform Background This paper (joint work with Steve Kusiak) extends the concept of scattering support to an inhomogeneous background medium.
A scattering support for broadband sparse far field measurements This paper (joint work with James Kelly) defines a notion of scattering support for far field measurements made at a few angles but many frequencies.
The Convex Back-scattering Support (joint work with Houssem Haddar and Steve Kusiak) formulates a convex scattering support for back-scattering.
Notions of Support for Far Fields extends the notion of convex scattering support from convex to Unions of Well-Separated Convex (UWSC) sets.

1D Inverse Scattering via Layer Splitting/Stripping

Some Transparencies which describe the main results from the papers below and an application to experimental data
Layer Stripping for the Helmholtz Equation (pdf) appeared in SIAM Journal of Applied Math. June 1996
Linear and Nonlinear Inverse Scattering (pdf) appeared in SIAM Journal of Applied Mathematics, 59 (2) pp. 669--699 April 1999
Layerstripping (pdf) appeared in Surveys on Solution Methods for Inverse Problems, Colton, Engl, Louis, McLaughlin, Editors, (2000)
A Matlab Program (GUI) to Layerstrip
- ls52_help.txt
- ls52.m

Some other Reprints and Preprints