My Publications

My Papers(pdf) -- in reverse chronological order

Some Preprints and Lectures by Topic

• Translation Invariant Estimates for Operators with Simple Characteristics -- joint work with Eemeli Blasten. We prove estimates for constant coefficient PDE's that are invariant under dilation, rotation, and translation.
• 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.

• Do Corner Always Scatter ? --- a joint paper with Eemeli Blasten and Lassi Paivarinta that shows that, for a domain with a right angle corner, and a contrast which doesn't vanish in a neighborhood of the corner (and real wavenumbers) , every incident wave produces a nontrivial scattered wave. Therefore, this domain has infinitely many real interior transmission eigenvalues, but no real transmisision eigenvalues.
• One dimensional Transmission Eigenvalues --- a complete description of all transmission eigenvalues for an interval with constant contrast.
• 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)

• Uncertainty Principles for inverse source problems in 3 dimensions --- joint paper with Roland Griesmaier
• Uncertainty Principles for inverse source problems and supplementary material --- joint paper with Roland Griesmaier
• Far field splitting by iteratively reweighted L^1 minimization --- joint paper with Roland Griesmaier
• Far Field Splitting for the Helmholtz Equation --- joint paper with Roland Griesmaier and Martin Hanke describing the the dependence of condition number of the linear operator that splits far fields radiated by two sources supported in disks in terms of the radii of the disks and the distance between them.
• 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 practical 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.

• 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 This pdf includes some small corrections. They are listed at the top of the paper. "/data/users/sylvest/papers/SIAP_0319771Corrected.pdf"
• 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

An Anisotropic Inverse Boundary Value Problem, CPAM 43, 201--232 (1990).

Inverse Boundary Value Problems: An Overview