James Ralston

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