Scattering maps for time-dependent Schrödinger operators on curved spaces with specific metrics determine the potential uniquely via the condition that they differ from another by a compact operator at a critical level.
The scattering map for the Schrodinger operator on curved spaces
5 Pith papers cite this work. Polarity classification is still indexing.
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Eigenfunctions of the Gaussian-weighted X-ray normal operator are joint eigenfunctions of the harmonic oscillator and spherical Laplacian, with spectrum related to 1-cusp elliptic pseudodifferential operators.
Scattering maps of the time-dependent Schrödinger equation determine the metric up to diffeomorphism pullback when the maps differ by a compact operator.
On metric cones, multiplicity of conjugate points within distance π on the boundary causes |t|^{1/2} loss in long-time decay and half-order regularity shift for Schrödinger dispersive estimates, except when the Legendre submanifold satisfies a proposed admissible condition.
Lecture notes summarizing non-elliptic Fredholm theory from a 2025 Australian winter school on microlocal analysis.
citing papers explorer
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Determining potentials from the scattering map of the time-dependent Schr\"odinger equation
Scattering maps for time-dependent Schrödinger operators on curved spaces with specific metrics determine the potential uniquely via the condition that they differ from another by a compact operator at a critical level.
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Gaussian-weighted normal operators on Euclidean space
Eigenfunctions of the Gaussian-weighted X-ray normal operator are joint eigenfunctions of the harmonic oscillator and spherical Laplacian, with spectrum related to 1-cusp elliptic pseudodifferential operators.
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Determining metrics from the scattering map of the time-dependent Schr\"odinger equation
Scattering maps of the time-dependent Schrödinger equation determine the metric up to diffeomorphism pullback when the maps differ by a compact operator.
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The effect of geometric focusing on dispersive estimates for Schr\"odinger and wave equations
On metric cones, multiplicity of conjugate points within distance π on the boundary causes |t|^{1/2} loss in long-time decay and half-order regularity shift for Schrödinger dispersive estimates, except when the Legendre submanifold satisfies a proposed admissible condition.
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Lecture notes on non-elliptic Fredholm theory
Lecture notes summarizing non-elliptic Fredholm theory from a 2025 Australian winter school on microlocal analysis.