email: ralston@math.ucla.edu

Office Phone: 310-825-4498

Recent Publications

Remark on spectral rigidity for magnetic Schroedinger operators (with G. Eskin), to appear in proceedings of the Mark Krein Centenary conference, Odessa, April 2007. pdf file

Inverse scattering for gratings and wave guides (with G. Eskin and M. Yamamoto) Inverse Problems Volume 24(2008), #2. pdf file

Inverse spectral problems in rectangular domains (with G. Eskin) CPDE Volume 32(2007), 971-1000 pdf file . Also Slides for a talk on this paper at Applied Inverse Problems 2007, Vancouver, June 29, 2007.

On effective Hamiltonians for adiabatic perturbations of magnetic Schroedinger operators (with M. Dimassi and J.-C. Guillot) pdf file , Asymptotic Analysis 40 (2004), 137-146.

Inverse Boundary Value Problems for Systems of Partial Differential Equations (with G. Eskin) pdf file , in Recent Developments in Theories & Numerics, Y-C. Hon, M. Yamamoto, J. Cheng and J-Y. Lee, Eds., pp. 105-113, World Scientific, New Jersey.

On the inverse problem for linear isotropic elasticity and Cauchy Riemann systems (with G. Eskin) pdf file . Contemporary Math. Volume 348 (2004), H. Isozaki, Ed., 53-69.

Lecture Notes

Notes for talk on Gliding Beams, Michigan State, March 2008 pdf file

Notes on Gaussian Beams (revised September 2005) pdf file .

Analysis Bootcamp, Summer 2009

Assignment 1 and Comments and Solutions

Assignment 2 and Comments and Solutions

Assignment 3 and Comments and Solutions

Assignment 4 and Comments and Solutions

Notes

Heine-Borel Compactness implies Bolzano-Weierstrass Compactness

A brief discussion of Dedekind Cuts

Equality of Mixed Partial Derivatives

The Inverse Function Theorem

Rearrangement of Series

Root Test vs Ratio Test

The Fundamental Theorems