Spectral and scattering inverse problems
- 1 December 1978
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 19 (12) , 2410-2425
- https://doi.org/10.1063/1.523645
Abstract
The reconstruction of a differential operator form discrete spectra is reduced to its reconstruction from an S‐matrix. This method makes it possible to solve the singular Sturm–Liouville problems which determine certain modes of a sphere. The results pave the way for handling studies in which information on modes and scattering results would all be taken into account. They are applied to the earth inverse problem and partial answers are given to a well‐known conjecture. Finally the relevance of the JWKB approximation in this kind of problem is briefly discussed.Keywords
This publication has 12 references indexed in Scilit:
- Impedance, zero energy wavefunction, and bound statesJournal of Mathematical Physics, 1977
- On the determination of the density of a vibrating string from spectral dataJournal of Mathematical Analysis and Applications, 1976
- Inverse problem for a vibrating beamZeitschrift für angewandte Mathematik und Physik, 1976
- A Discrete Model of the Inverse Love Wave ProblemGeophysical Journal International, 1976
- The inverse problem of scattering theory and Riemann's methodIl Nuovo Cimento A (1971-1996), 1972
- On the effective determination of the wave operator from given spectral data in the case of a difference equation corresponding to a Sturm-Liouville differential equationJournal of Mathematical Analysis and Applications, 1970
- Derivation of Nonrelativistic Sum Rules from the Causality Condition of Wigner and Van KampenJournal of Mathematical Physics, 1968
- Numerical Applications of a Formalism for Geophysical Inverse ProblemsGeophysical Journal International, 1967
- Can One Hear the Shape of a Drum?The American Mathematical Monthly, 1966
- Oscillations of the earthProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1959