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Bulletin of the American Mathematical Society

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Book Review

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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?)

  • Wolfgang Arendt, Paul R. Chernoff, and Tosio Kato, A generalization of dissipativity and positive semigroups, J. Operator Theory 8 (1982), no. 1, 167–180. MR 670183
  • A. V. Balakrishnan, Applied functional analysis, 2nd ed., Applications of Mathematics, vol. 3, Springer-Verlag, New York-Berlin, 1981. MR 612793
  • Charles J. K. Batty and Derek W. Robinson, Positive one-parameter semigroups on ordered Banach spaces, Acta Appl. Math. 2 (1984), no. 3-4, 221–296. MR 753696,
  • Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York Inc., New York, 1967. MR 0230022
  • Aldo Belleni-Morante, Applied semigroups and evolution equations, The Clarendon Press, Oxford University Press, New York, 1979. Oxford Mathematical Monographs. MR 548865
  • Ola Bratteli, Derivations, dissipations and group actions on 𝐶*-algebras, Lecture Notes in Mathematics, vol. 1229, Springer-Verlag, Berlin, 1986. MR 871870
  • [BrJ] O. Bratteli and P. E. T. Jørgensen (eds. ), Positive semigroups of operators, and applications, D. Reidel Publishing Company, 1984.
  • Ola Bratteli and Derek W. Robinson, Operator algebras and quantum-statistical mechanics. II, Springer-Verlag, New York-Berlin, 1981. Equilibrium states. Models in quantum-statistical mechanics; Texts and Monographs in Physics. MR 611508
  • Paul R. Chernoff, Product formulas, nonlinear semigroups, and addition of unbounded operators, American Mathematical Society, Providence, R. I., 1974. Memoirs of the American Mathematical Society, No. 140. MR 0417851
  • [vC] J. A. van Casteren, Generators of strongly continuous semigroups, Pitman Press, 1985.
  • Edward Brian Davies, One-parameter semigroups, London Mathematical Society Monographs, vol. 15, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. MR 591851
  • Hector O. Fattorini, The Cauchy problem, Encyclopedia of Mathematics and its Applications, vol. 18, Addison-Wesley Publishing Co., Reading, Mass., 1983. With a foreword by Felix E. Browder. MR 692768
  • H. O. Fattorini, Second order linear differential equations in Banach spaces, North-Holland Mathematics Studies, vol. 108, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 99. MR 797071
  • William G. Faris, Self-adjoint operators, Lecture Notes in Mathematics, Vol. 433, Springer-Verlag, Berlin-New York, 1975. MR 0467348
  • Avner Friedman, Partial differential equations, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1969. MR 0445088
  • Jerome A. Goldstein, Semigroups of linear operators and applications, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1985. MR 790497
  • Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
  • Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • Tosio Kato, Linear evolution equations of “hyperbolic” type, J. Fac. Sci. Univ. Tokyo Sect. I 17 (1970), 241–258. MR 0279626
  • S. G. Kreĭn, Linear differential equations in Banach space, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by J. M. Danskin; Translations of Mathematical Monographs, Vol. 29. MR 0342804
  • W. Arendt, A. Grabosch, G. Greiner, U. Groh, H. P. Lotz, U. Moustakas, R. Nagel, F. Neubrander, and U. Schlotterbeck, One-parameter semigroups of positive operators, Lecture Notes in Mathematics, vol. 1184, Springer-Verlag, Berlin, 1986. MR 839450
  • A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486
  • G. Peano, Intégration par séries des équations différentielles linéaires, Math. Ann. 32 (1888), no. 3, 450–456 (French). MR 1510521,
  • [T] H. Tannabe, Equations of evolution, Pitman Press, 1979.
  • Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913
  • Samuel D. Zaidman, Abstract differential equations, Research Notes in Mathematics, vol. 36, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. MR 569750

Review Information:

Reviewer: Ola Bratteli
Journal: Bull. Amer. Math. Soc. 18 (1988), 100-103