Asymptotic perturbation series
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References
- Kurt Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann. 109 (1934), no. 1, 465–487 (German). MR 1512905, DOI 10.1007/BF01449150
- Kurt Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann. 109 (1934), no. 1, 685–713 (German). MR 1512919, DOI 10.1007/BF01449164
- Tosio Kato, On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4 (1949), 334–339. MR 38738, DOI 10.1143/JPSJ.4.334 On the convergence of the perturbation method, J. Fac. Sci. Imp. Univ. Tokyo. Sect. I vol. VI, part 3, pp. 145-226.
- Tosio Kato, Perturbation theory of semi-bounded operators, Math. Ann. 125 (1953), 435–447. MR 54854, DOI 10.1007/BF01343135 On the adiabatic theorem of quantum mechanics, Journal of the Physical Society of Japan vol. 5 (1950) pp. 435-439.
- Vernon A. Kramer, Asymptotic inverse series, Proc. Amer. Math. Soc. 7 (1956), 429–437. MR 82659, DOI 10.1090/S0002-9939-1956-0082659-8
- Béla de Sz. Nagy, Perturbations des transformations autoadjointes dans l’espace de Hilbert, Comment. Math. Helv. 19 (1947), 347–366 (French). MR 20722, DOI 10.1007/BF02565964 C. Pauling and E. B. Wilson 1. Introduction to quantum mechanics, New York, 1935. Lord Rayleigh 1. Theory of sound I, 2d ed. rev., London, 1927, Macmillan.
- Franz Rellich, Störungstheorie der Spektralzerlegung, Math. Ann. 113 (1937), no. 1, 600–619 (German). MR 1513109, DOI 10.1007/BF01571652
- Franz Rellich, Störungstheorie der Spektralzerlegung, Math. Ann. 113 (1937), no. 1, 677–685 (German). MR 1513115, DOI 10.1007/BF01571658 III. Math. Ann. vol. 116 (1939) pp. 555-570.
- Franz Rellich, Störungstheorie der Spektralzerlegung. IV, Math. Ann. 117 (1940), 356–382 (German). MR 2715, DOI 10.1007/BF01450023
- Franz Rellich, Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung, Math. Ann. 122 (1951), 343–368 (German). MR 43316, DOI 10.1007/BF01342848
- Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877, DOI 10.1090/coll/015
- E. C. Titchmarsh, Some theorems on perturbation theory, Proc. Roy. Soc. London Ser. A 200 (1949), 34–46. MR 34495, DOI 10.1098/rspa.1949.0157
- František Wolf, Analytic perturbation of operators in Banach spaces, Math. Ann. 124 (1952), 317–333. MR 50167, DOI 10.1007/BF01343573
Additional Information
- © Copyright 1957 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 85 (1957), 88-105
- MSC: Primary 46.2X
- DOI: https://doi.org/10.1090/S0002-9947-1957-0087912-5
- MathSciNet review: 0087912