On the perturbation theory of closed linear operators

Tosio KATO

doi:10.2969/jmsj/00430323

Tosio KATO

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1952 Volume 4 Issue 3-4 Pages 323-337

DOI https://doi.org/10.2969/jmsj/00430323

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Published: 1952 Received: September 01, 1952 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Right : [1] Heinz, E.: Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann. 123 (1951), 415-438.
[2] Hille, E.: Functional analysis and semi-groups, New York, 1948.
[3] Kato, T.: On the convergence of the perturbation method, I, Progress of Theoretical Physics 4 (1949), 514-523.
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[5] Kato, T.: Perturbation theory of linear operators (in Japanese), Sugaku (Mathematics) 2 (1950), 201-208.
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[7] Kato, T.: On the convergence of the perturbation method, J. Fac. Sci. Univ. Tokyo, Section I, vol. 6 (1951), 145-226.
[8] Kato, T.: Perturbation theory of semi-bounded operators, Math. Ann. (in press).
[9] Nagumo, M.: Einige alalytische Untersuchungen in linearen metrischen Ringen, Jap. J. Math. 13 (1936), 61-80.
[10] Rellich, F.: Störungstheorie der Spektralzerlegung, I. Mitt., Math. Ann. 113 (1937), 600-619.
[11] Rellich, F.: II. Mitt., Math. Ann. 113 (1937), 677-685.
[12] Rellich, F.: III. Mitt., Math. Ann. 116 (1939), 555-570.
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[14] Rellich, F.: V. Mitt., Math. Ann. 118 (1941/43), 462-484.
[15] Sz.-Nagy, B. v.: Spektraldarstellung linearer Transformationen des Hilbertschen Raumes, Erg. Math. 5 (1942), 416-496.
[16] Sz.-Nagy, B. v.: Perturbations des transformations autoadjointes dans l'espace de Hilbert, Comment. Math. Helv. 19 (1946/47), 347-366.
[17] Sz.-Nagy, B. v.: Perturbations des transformations linéaires fermées, Acta Sci. Math. Szeged 14 (1951), 125-137.
[18] Titchmarsh, E. C.: Some theorems on perturbation theory, Proc. Roy. Soc. A200 (1949), 34-46.
[19] Titchmarsh, E. C.: II, Proc. Roy. Soc. A201 (1950), 473-479.
[20] Titchmarsh, E. C.: III, Proc. Roy. Soc. A207 (1951), 321-328.

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