An inverse problem for the space–time fractional Schrödinger equation on closed manifolds
Abstract
Abstract We formulate an inverse problem for an uncoupled space–time fractional Schrödinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the knowledge of the associated source-to-solution map. Our argument relies on the asymptotic behavior of Mittag-Leffler functions, Weyl’s law for the eigenvalues of the Laplace–Beltrami operator, the unique continuation property of the space-fractional operator and the disjoint data metric determination result for the wave equation. We also provide a probabilistic formulation of our inverse problem.
Fields of Study & Subjects
Numerical methods in inverse problems
advanced mathematical theories
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Canadian Mathematical Bulletin
- Publisher
- Canadian Mathematical Society
- Pages
- 1–15
- Publication date
- 4 June 2026
- Language
- EN