Fractional powers of dissipative operators

Tosio KATO

doi:10.2969/jmsj/01330246

Tosio KATO

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1961 Volume 13 Issue 3 Pages 246-274

DOI https://doi.org/10.2969/jmsj/01330246

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Published: 1961 Received: March 24, 1961 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] A. V. Balakrishnan, An operator calculus for infinitesimal generators of semigroups, Trans. Amer. Math. Soc., 91 (1959), 330-353.
[2] A. V. Balakrishnan, Fractional powers of closed operators and the semigroups generated by them, Pac. J. Math., 10 (1960), 419-437.
[3] K. O. Friedrichs. Spektraltheorie halbbeschränkter Operatoren and Anwendungen auf die Spektralzerlegung von Differentialoperatoren, I, Math. Ann., 109 (1934), 465-487.
[4] K. O. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math., 11 (1958), 333-418.
[5] V. P. Glushko and S. G. Krein, Fractional powers of differential operators and the imbedding theorems, Doklady Akad. Nauk, 122 (1958), 963-966. (Russian)
[6] E. Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann., 123 (1951), 415-438.
[7] T. Kato, Notes on some inequalities for linear operators, Math. Ann., 125 (1952), 208-212.
[8] T. Kato, Quadratic forms in Hilbert spaces and asymptotic perturbation series, Technical Report No. 7, Contract DA-04-200-ORD-171, University of California. 1955.
[9] T. Kato, Note on fractional powers of linear operators, Proc. Japan Acad., 36 (1960), 94-96.
[10] T. Kato, Estimation of iterated matrices, with application to the von Neumann condition, Numer. Math., 2 (1960), 22-29.
[11] T. Kato, Abstract evolution equations of parabolic type in Banach and Hilbert spaces, Nagoya Math. J. (1961), to be pulished.
[12] M. A. Krasnosel'skii and E. I. Pustylnik, The use of fractional powers of operators in studying Fourier series of eigenfunctions of differential operators, Doklady Akad. Nauk., 122 (1958), 978-981. (Russian)
[13] M. A. Krasnosel'skii and P. E. Sobolevskii, Fractional power of operators defined on Banach spaces, Doklady Akad. Nauk, 129 (1959), 499-502. (Russian)
[14] P. D. Lax and A. N. Milgram, Parabolic equations, Contributions to the Theory of Partial Differential Equations, Annals of Mathematics Studies, No. 33, pp. 167-190, Princeton, 1954.
[15] R. S. Phillips, Dissipative operators and hyperbolic systems of partial differential equations, Trans. Amer. Math. Soc., 90 (1959), 193-254.
[16] R. S. Phillips, Dissipative operators and parabolic partial differential equations, Comm. Pure Appl. Math., 12 (1959), 249-276.
[17] P. E. Sobolevskii, On equations with operators forming an acute angle, Doklady Akad. Nauk, 116 (1957), 754-757. (Russian)
[18] M. Z. Solomiak, The application of the semigroup theory to the study of differential equations in Banach spaces, Doklady Akad. Nauk, 122 (1958), 766-769. (Russian)
[19] K. Yosida, Fractional powers of infinitesimal generators and the analyticity of the semi-groups generated by them, Proc. Japan Acad., 36 (1960), 86-89.

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