Past and future of inverse problems
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Publication:2738032
DOI10.1063/1.533336zbMath0982.34010OpenAlexW2093334127MaRDI QIDQ2738032
Publication date: 30 August 2001
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.533336
Inverse problems for PDEs (35R30) Inverse scattering problems in quantum theory (81U40) Inverse problems involving ordinary differential equations (34A55) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Numerical solution of inverse problems involving ordinary differential equations (65L09)
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Cites Work
- A global uniqueness theorem for an inverse boundary value problem
- Reconstructions from boundary measurements
- The Gelfand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems
- Inverse scattering in one-dimensional nonconservative media
- Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials
- Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
- Elbow scattering and inverse scattering applications to LKdV and KdV
- On the integrability of linear and nonlinear partial differential equations
- The limited-view problem in diffraction tomography
- Joint inversion: a structural approach
- On the determination of a differential equation from its spectral function
- Some comments on Fourier analysis, uncertainty and modeling
- Layer-stripping solutions of multidimensional inverse scattering problems
- An optimal design problem for submerged bodies
- Can One Hear the Shape of a Drum? Revisited
- A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
- Construction of Potentials from the Phase Shifts at Fixed Energy
- On the spectral functions of the string
- Inverse scattering on the line
- The integrated inverse gravimetric-tomographic problem: a continuous approach
- The solution of certain initial boundary-value problems for the linearized Korteweg—deVries equation
- Inverse problems with structural prior information
- New situation in quantum mechanics (wonderful potentials from the inverse problem)
- On the Schrödinger equation with steplike potentials
- Inversion of Reflectivity Data for Nondecaying Potentials
- Applications of generalized stress in elastodynamics
- Modified gradient approach to inverse scattering for binary objects in stratified media
- Nonuniqueness in inverse problems
- Linear inverse problems with discrete data. I. General formulation and singular system analysis
- Mathematical Morphology: A Modern Approach in Image Processing Based on Algebra and Geometry
- A patchwork approach to problems with boundary measurements
- Huygens' principle and integrability
- Quasi-Monte Carlo integration over for migration inversion
- Resonance Phenomena in Local Perturbations of Parallel-plane Waveguides
- Can One Hear the Shape of a Drum?
- Analytic Properties of a Class of Potentials and the Corresponding Jost Functions
- Remarks on the Determination of a Central Field of Force from the Elastic Scattering Phase Shifts
- An Iteration Formula for Fredholm Integral Equations of the First Kind
- Equivalent Potentials
- Certain Explicit Relationships between Phase Shift and Scattering Potential
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