Pacific Journal of Mathematics

Fractional powers of operators.

Hikosaburo Komatsu

Article information

Source
Pacific J. Math., Volume 19, Number 2 (1966), 285-346.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102993838

Mathematical Reviews number (MathSciNet)
MR0201985

Zentralblatt MATH identifier
0154.16104

Subjects
Primary: 47.50

Citation

Komatsu, Hikosaburo. Fractional powers of operators. Pacific J. Math. 19 (1966), no. 2, 285--346. https://projecteuclid.org/euclid.pjm/1102993838


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References

  • [1] A. V. Balakrishnan, An operational calculus for infinitesimalgenerators of semi- groups, Trans. Amer. Math. Soc. 91 (1959), 330-353.
  • [2] A. V. Balakrishnan, Fractional powers of closed operators and the semi-groups generated by them, Pacific J. Math. 10 (1960), 419-437.
  • [3] H. Fujita and T. Kato, On the Naier-Stokes initial value problem, I, Arch. Rat. Mech. Anal. 16 (1964), 269-315.
  • [4] G. H. Hardy, Weierstrass's non-differentiable function,Trans. Amer. Math. Soc. 17 (1916), 301-325.
  • [5] G. H. Hardy and J. E. Littlewood, Some properties of fractionalintegrals, I, Math. Z., 27 (1928), 565-606, II, ibd. 34 (1932), 403-439.
  • [6] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ. 31.
  • [7] K. Hoffman, Banach spaces of analytic functions, Prentice Hall, 1962.
  • [8] S. It, The existence and the uniqueness of regular solution of non-stationary Navier- Stokes equation, J. Fac. Sci. Univ. Tokyo, Sec. I 9 (1961), 103-140.
  • [9] T. Kato, Remarks on pseudo-resolvents and infinitesimalgenerators of semi-groups,
  • [10] T. Kato, Note on fractional powers of linear operators, Proc. Japan Acad. 36 (1960), 94-96.
  • [11] T. Kato, Fractional powers of dissipative operators, J. Math. Soc. Japan 13 (1961), 246-274.
  • [12] H. Komatsu, Semi-groups of operators in locally convex spaces, J. Math. Soc. Japan 16 (1964), 230-262.
  • [13] M. A. Krasnoseskii and P. E. Sobolevskii, Fractional powers of operators acting in Banach spaces, Doklady Akad. Nauk SSSR 129 (1959), 499-502.
  • [14] E. R. Love and L. C. Young, On fractional integrationby parts, Proc. London Math. Soc. 44 (1938), 1-35.
  • [15] L. Nirenberg, On elliptic partial differential equation, Ann. Scu. Norm. Sup. Pisa, Ser. Ill 13 (1959), 115-162.
  • [16] R. S. Phillips, On the generation of semi-groups of linear operators, Pacific J. Math. 2 (1952), 343-369.
  • [17] M. Sato, Theory of hyperfunctions, I, J, Fac. Sci. Univ. Tokyo, Sec. 1 8 (1959), 139-193, II, ibd. 8 (1960), 387-437.
  • [18] A. E. Taylor, Spectral theory of closeddistributive operators, Acta Math. 84 (1950), 189-224.
  • [19] H. F. Trotter, Approximationof semi-groups of operators, Pacific J. Math. 8 (1958), 887-919.
  • [20] J. Watanabe, On some properties of fractional powers of linear operators, Proc. Japan Acad. 37 (1961), 273-275.
  • [21] K. Yosida, On the differentiabilityof semi-groups of linear operators, Proc. Japan Acad. 34 (1958), 337-340.
  • [22] K. Yosida, Fractional powers of infinitesimal generators and the analyticity of the semi-groups generated by them, Proc. Japan Acad. 36 (1960), 86-89.
  • [23] K. Yosida, Ergodic theorem for pseudo-resolvents, Proc. Japan Acad. 37 (1961),422- 425.
  • [24] A. Zygmund, Trigonometrical series, Warszawa, 1935.

See also

  • II : Hikosaburo Komatsu. Fractional powers of operators. II. Interpolation spaces. Pacific Journal of Mathematics volume 21, issue 1, (1967), pp. 89-111.
  • Hikosaburo Komatsu. Fractional powers of operators. {III}. Negative powers. III [MR 39 #3340] J. Math. Soc. Japan 21 1969 205--220.
  • Hikosaburo Komatsu. Fractional powers of operators. {IV}. Potential operators. IV [MR 39 #3341] J. Math. Soc. Japan 21 1969 221--228.
  • Hikosaburo Komatsu. Fractional powers of operators. V. Dual operators. V [MR 42 #6650] J. Fac. Sci. Univ. Tokyo Sect. I 17 1970 373--396.
  • Hikosaburo Komatsu. Fractional powers of operators. {VI}. Interpolation of non-negative operators and imbedding theorems. VI [MR 47 #7510] J. Fac. Sci. Univ. Tokyo Sect. IA Math. 19 1972 1--63.