Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF
Book Information:

Author: Jerome A. Goldstein
Title: Semigroups of linear operators and applications
Additional book information: Oxford Mathematical Monographs, Oxford University Press, Clarendon Press, New York and Oxford, 1985, x + 245 pp., $42.50. ISBN 0-19-503540-2.

References [Enhancements On Off] (What's this?)

  • [ACK] W. Arendt, P. R. Chernoff and T. Kato, A generalization of dissipativity and positive semigroups, J. Operator Theory 8 (1982), 167-180. MR 670183
  • [Ba] A. V. Balakrishnan, Applied functional analysis, second ed., Springer-Verlag, 1981. MR 612793
  • [BaR] C. J. K. Batty and D. W. Robinson, Positive one-parameter semigroups on ordered Banach spaces, Acta Appl. Math. 1 (1984), 221-296. MR 753696
  • [BB] P. L. Butzer and H. Berens, Semi-groups of operators and approximation, Grundlehren Math. Wiss., Band 145, Springer-Verlag, Berlin and New York, 1967. MR 230022
  • [B-M] A. Belleni-Morante, Applied semigroups and evolution equations, Clarendon Press, 1979. MR 548865
  • [Br] O. Bratteli, Derivations, dissipations and groups actions on C* -algebras, Lecture Notes in Math., vol. 1229, Springer-Verlag, Berlin and New York, 1986. MR 871870
  • [BrJ] O. Bratteli and P. E. T. Jørgensen (eds. ), Positive semigroups of operators, and applications, D. Reidel Publishing Company, 1984.
  • [BrR] O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics. I, second ed., Springer-Verlag, Berlin and New York, 1987. MR 611508
  • [C] P. R. Chernoff, Product formulas, non-linear semigroups and addition of unbounded operators, Mem. Amer. Math. Soc., no. 140 (1974). MR 417851
  • [vC] J. A. van Casteren, Generators of strongly continuous semigroups, Pitman Press, 1985.
  • [D] E. B. Davies, One-parameter semigroups, Academic Press, 1980. MR 591851
  • [F1] H. O. Fattorini, The Cauchy problem, Addison-Wesley, 1983. MR 692768
  • [F2] H. O. Fattorini, Second order linear differential equations in Banach spaces, North-Holland, 1985. MR 797071
  • [Fa] W. G. Faris, Self-adjoint operators, Lecture Notes in Math., vol. 433, Springer-Verlag, Berlin and New York, 1975. MR 467348
  • [Fr] A. Friedman, Partial differential equations, Holt, Rinehart and Winston, 1969. MR 445088
  • [G] J. A. Goldstein, Semigroups of linear operators and applications, Oxford Univ. Press/ Clarendon Press, 1985. MR 790497
  • [HP] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., no. 31, Amer. Math. Soc., Providence, R. I., 1957. MR 89373
  • [Kl] T. Kato, Perturbation theory for linear operators, Grundlehren Math. Wiss., Band 132, Springer-Verlag, Berlin and New York, 1966. MR 203473
  • [K2] T. Kato, Linear evolution equations of "hyperbolic" type, J. Fac. Sci. Univ. Tokyo 17 (1970), 241-258. MR 279626
  • [Kr] S. G. Krein, Linear differential equations in Banach space, Transl. Math. Monographs, vol. 29, Amer. Math. Soc., Providence, R. I., 1971. MR 342804
  • [N] R. Nagel (ed. ), One-parameter semigroups of positive operators, Lecture Notes in Math., vol. 1184, Springer-Verlag, Berlin and New York, 1986. MR 839450
  • [Pa] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Math. Sciences, vol. 44, Springer-Verlag, Berlin and New York, 1983. MR 710486
  • [Pe] G. Peano, Intégration par séries des équations différentielles linéaires, Math. Ann. 32 (1888), 450-456. An earlier version appeared in Atti. Accad. Sci. Torino, 20 February, 1887. MR 1510521
  • [T] H. Tannabe, Equations of evolution, Pitman Press, 1979.
  • [Y] K. Yosida, Functional analysis, 6th ed., Springer-Verlag, 1980. MR 617913
  • [Z] S. D. Zaidman, Abstract differential equations, Pitman Press, 1979. MR 569750

Review Information:

Reviewer: Ola Bratteli
Journal: Bull. Amer. Math. Soc. 18 (1988), 100-103
DOI: http://dx.doi.org/10.1090/S0273-0979-1988-15621-2