On the spectra of unitary half-scattering operators
Author:
C. R. Putnam
Journal:
Quart. Appl. Math. 20 (1962), 85-88
MSC:
Primary 81.47
DOI:
https://doi.org/10.1090/qam/138365
MathSciNet review:
138365
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Additional Information
- N. Aronszajn, On a problem of Weyl in the theory of singular Sturm-Liouville equations, Amer. J. Math. 79 (1957), 597–610. MR 88623, DOI https://doi.org/10.2307/2372564
- J. M. Cook, Convergence to the Møller wave-matrix, J. Math. and Phys. 36 (1957), 82–87. MR 91746, DOI https://doi.org/10.1002/sapm195736182
K. O. Friedrichs, Über die Spektralzerlegung eines Integraloperators, Math. Ann. 115, 249–272 (1938)
- K. O. Friedrichs, On the perturbation of continuous spectra, Communications on Appl. Math. 1 (1948), 361–406. MR 29100, DOI https://doi.org/10.1002/cpa.3160010404
- K. O. Friedrichs, Mathematical aspects of the quantum theory of fields, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1953. MR 0056468
M. N. Hack, On convergence to the Moller wave operators, Nuovo Cimento 9, 731–733 (1958)
- J. M. Jauch, Theory of the scattering operator, Helv. Phys. Acta 31 (1958), 127–158. MR 94163
- J. M. Jauch and I. I. Zinnes, The asymptotic condition for simple scattering systems, Nuovo Cimento (10) 11 (1959), 553–567 (English, with Italian summary). MR 107498
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- Tosio Kato, Perturbation of continuous spectra by trace class operators, Proc. Japan Acad. 33 (1957), 260–264. MR 92133
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S. T. Kuroda, On the existence and the unitary property of the scattering operator, Nuovo Cimento 12, 431–454 (1959)
- C. R. Putnam, Commutators and absolutely continuous operators, Trans. Amer. Math. Soc. 87 (1958), 513–525. MR 100226, DOI https://doi.org/10.1090/S0002-9947-1958-0100226-0
C. R. Putnam, Commutators, perturbations, and unitary spectra, Acta Mathematica (to appear)
- Marvin Rosenblum, Perturbation of the continuous spectrum and unitary equivalence, Pacific J. Math. 7 (1957), 997–1010. MR 90028
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A. Winter, Small perturbations, Am. J. Math. 67, 417–430 (1945)
H. Weyl, Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen, Math. Ann. 68, 220–269 (1910)
N. Aronszajn, On a problem of Weyl in the theory of singular Sturm-Liouville equations, Am. J. Math. 79, 597–610 (1957)
J. M. Cook, Convergence to the Moller wave-matrix, J. Math, and Phys. 36, 82–87 (1957)
K. O. Friedrichs, Über die Spektralzerlegung eines Integraloperators, Math. Ann. 115, 249–272 (1938)
K. O. Friedrichs, On the perturbation of continuous spectra, Communs. Appl. Math. 1, 361–401 (1948)
K. O. Friedrichs, Mathematical aspects of the quantum theory of fields, Interscience Publ., New York, 1953.
M. N. Hack, On convergence to the Moller wave operators, Nuovo Cimento 9, 731–733 (1958)
J. M. Jauch, Theory of the scattering operator, Helv. Phys. Acta 31, 127–158 (1958)
J. M. Jauch and I. I. Zinnes, The asymptotic condition for simple scattering systems, Nuovo Cimento 11, 553–567 (1959)
T. Kato, On finite-dimensional perturbations of self-adjoint operators, J. Math. Soc. Japan 9, 239–249 (1957)
T. Kato, Perturbation of continuous spectra by trace class operators, Proc. Japan Acad. 33, 260–264 (1957)
K. Kodaira, The eigenvalue problem for ordinary differential equations of the second order and Heisenberg’s theory of S-matrices. Am. J. Math. 71, 921–945 (1949)
S. T. Kuroda, On the existence and the unitary property of the scattering operator, Nuovo Cimento 12, 431–454 (1959)
C. R. Putnam, Commutators and absolutely continuous operators, Trans. Am. Math. Soc. 87, 513–525 (1958)
C. R. Putnam, Commutators, perturbations, and unitary spectra, Acta Mathematica (to appear)
M. Rosenblum, Perturbation of the continuous spectrum and unitary equivalence, Pacific J. Math. 7, 997–1010 (1957)
E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations, Oxford, 1946
A. Winter, Small perturbations, Am. J. Math. 67, 417–430 (1945)
H. Weyl, Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen, Math. Ann. 68, 220–269 (1910)
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Article copyright:
© Copyright 1962
American Mathematical Society