Pacific Journal of Mathematics

A note on fractional derivatives of semigroups and cosine functions.

H. O. Fattorini

Article information

Source
Pacific J. Math., Volume 109, Number 2 (1983), 335-347.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102720105

Mathematical Reviews number (MathSciNet)
MR721925

Zentralblatt MATH identifier
0524.47026

Subjects
Primary: 47D05

Citation

Fattorini, H. O. A note on fractional derivatives of semigroups and cosine functions. Pacific J. Math. 109 (1983), no. 2, 335--347. https://projecteuclid.org/euclid.pjm/1102720105


Export citation

References

  • [1] A. V. Balakrishnan, Fractional powers of closed operators and the semi-groupsgener- ated by them, Pacific J. Math., 10 (1960), 419-437.
  • [2] J. W. Dettman,Saturation theorems connected with the abstract wave equation, SIAM J. Math. Anal., 9 (1978), 54-64.
  • [3] N. Dunford and J. T. Schwartz, Linear Operators, part I, Wiley-Interscience, New York, 1958.
  • [4] H. O. Fattorini, Ordinary differential equations in linear topological spaces /, J. Differential Equations, 5 (1969), 72-105.
  • [5] H. O. Fattorini, Ordinary differential equations in linear topological spaces II, J. Differential Equations, 6 (1969), 50-70.
  • [6] H. O. Fattorini, Some remarks on second order abstract Cauchy problems, Funkcialaj Ekvacioj, 24(1981), 331-344.
  • [7] I. S. Gradstein and I. M. Ridzyk, Tables of Integrals, Sums, Series and Derivatives, Goztekhizdat, Moscow, 1963.
  • [8] J. Kisyski, On operator-valued solutions of D'Alembert'sfunctional equation, II, Studia Math.,42 (1972), 43-66.
  • [9] H. Komatsu, Fractionalpowers of operators, Pacific J. Math., 19 (1966), 285-346.
  • [10] S. G. Krein, Linear Differential Equations in Banach Spaces, Izdat. "Nauka", Moscow, 1967. English translation: Amer. Math. Soc. Trans. Math. Monog., vol. 29, Providence, 1971.
  • [11] M. Sova, Cosine operatorfunctions, Rozprawy Mat., 49 (1966), 1-47.
  • [12] M. Sova, Equations hyperboliques avec petit parametre dans les espaces de Banach generaux, Colloq. Math., 21 (1970), 303-320.
  • [13] M. Sova, Encore sur les equations hyperboliques avec petit parametre dans les espaces de Banach generaux, Colloq. Math., 25 (1972), 135-161.
  • [14] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1944.
  • [15] K. Yosida, Functional Analysis, 5th ed., Springer, Berlin, 1978.
  • [16] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, 1959.