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Award ID contains: 2205266

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  1. ; ; (, SIAM Journal on Imaging Sciences)
    Free, publicly-accessible full text available September 30, 2026
  2. ; (, Journal of Spectral Theory)
    We study the asymptotic behavior of the counting function of negative eigenvalues of Schrödinger operators with real valued potentials which decay at infinity on asymptotically hyperbolic manifolds. We establish conditions on the rate of decay of the potential that determine if there are finitely or infinitely many negative eigenvalues. In the latter case, they may only accumulate at zero and we obtain the asymptotic behavior of the counting function of eigenvalues in an interval(-\infty, -E)asE\rightarrow 0. 
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    Free, publicly-accessible full text available May 13, 2026
  3. ; (, SIAM Journal on Imaging Sciences)
    Free, publicly-accessible full text available March 31, 2026
  4. (, Annales Henri Poincaré)
    Free, publicly-accessible full text available February 8, 2026
  5. (, SIAM Journal on Mathematical Analysis)
    Free, publicly-accessible full text available December 31, 2025
  6. (, De Gruyter)
    Full Text Available 
  7. ; (, SIAM Journal on Mathematical Analysis)
    Full Text Available 
  8. ; (, Communications in Mathematical Physics)
    Full Text Available 
  9. (, Inverse Problems)
    Abstract We consider the Cauchy problem and the source problem for normally hyperbolic operators on the Minkowski spacetime, and study the determination of solutions from their integrals along light-like geodesics. For the Cauchy problem, we give a new proof of the stable determination result obtained by Vasy and Wang (2021 Commun. Math. Phys. 384 503–32). For the source problem, we obtain stable determination for sources with space-like singularities. Our proof is based on the microlocal analysis of the normal operator of the light ray transform composed with the parametrix for strictly hyperbolic operators. 
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