A note on an inverse problem in mathematical physics
Authors:
Richard Bellman and John M. Richardson
Journal:
Quart. Appl. Math. 19 (1961), 269-271
MSC:
Primary 34.30
DOI:
https://doi.org/10.1090/qam/130417
MathSciNet review:
130417
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Additional Information
- Göran Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte, Acta Math. 78 (1946), 1–96 (German). MR 15185, DOI https://doi.org/10.1007/BF02421600
- I. M. Gel′fand and B. M. Levitan, On the determination of a differential equation from its spectral function, Amer. Math. Soc. Transl. (2) 1 (1955), 253–304. MR 0073805
- Irvin Kay, The inverse scattering problem when the reflection coefficient is a rational function, Comm. Pure Appl. Math. 13 (1960), 371–393. MR 114540, DOI https://doi.org/10.1002/cpa.3160130304
E. A. Guillemin, A summary of modern methods of network synthesis, Advances in Electronics, Academic Press Inc., vol. 3, 1951, pp. 261–303
L. Weinberg, Linear network synthesis, McGraw-Hill Book Co., Inc., New York, to appear
L. Weinberg and P. Slepian, Realizability conditions on n-port networks, IRE Trans. on Circuit Theory, CT–5, 217–221 (1958)
- Eugene P. Wigner, On a class of analytic functions from the quantum theory of collisions, Ann. of Math. (2) 53 (1951), 36–67. MR 39059, DOI https://doi.org/10.2307/1969342
- A. M. Lane and R. G. Thomas, $R$-matrix theory of nuclear reactions, Rev. Mod. Phys. 30 (1958), 257–353. MR 0097255, DOI https://doi.org/10.1103/revmodphys.30.257
G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwerte Aufgabe, Acta Math. 78, 1–96 (1946)
I. M. Gelfand and B. M. Levitan, On the determination of a differential equation from its spectral function, Trans. Amer. Math. Soc. 2, 253–304 (1955)
I. Kay, The inverse scattering problem when the reflection coefficient is a rational function, Communs. Pure Appl. Math. 13, 371–406 (1960)
E. A. Guillemin, A summary of modern methods of network synthesis, Advances in Electronics, Academic Press Inc., vol. 3, 1951, pp. 261–303
L. Weinberg, Linear network synthesis, McGraw-Hill Book Co., Inc., New York, to appear
L. Weinberg and P. Slepian, Realizability conditions on n-port networks, IRE Trans. on Circuit Theory, CT–5, 217–221 (1958)
E. Wigner, On a class of analytic functions from the quantum theory of collisions, Ann. Math. 53, 36–67 (1951)
A. M. Lane and R. G. Thomas, R-matrix theory of nuclear reactions, Revs. Mod. Phys. 30, 257–352 (1958)
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Article copyright:
© Copyright 1961
American Mathematical Society
