Bulletin of the American Mathematical Society

MathSciNet review: 1567669
Full text of review: PDF   This review is available free of charge.
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.

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, DOI 10.1007/BF02280855

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, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 548865

Ola Bratteli, Derivations, dissipations and group actions on $C^*$-algebras, Lecture Notes in Mathematics, vol. 1229, Springer-Verlag, Berlin, 1986. MR 871870, DOI 10.1007/BFb0098817

[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, Texts and Monographs in Physics, Springer-Verlag, New York-Berlin, 1981. Equilibrium states. Models in quantum-statistical mechanics. MR 611508

Paul R. Chernoff, Product formulas, nonlinear semigroups, and addition of unbounded operators, Memoirs of the American Mathematical Society, No. 140, American Mathematical Society, Providence, R.I., 1974. 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 279626

S. G. Kreĭn, Linear differential equations in Banach space, Translations of Mathematical Monographs, Vol. 29, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by J. M. Danskin. 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, DOI 10.1007/BFb0074922

A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1

G. Peano, Intégration par séries des équations différentielles linéaires, Math. Ann. 32 (1888), no. 3, 450–456 (French). MR 1510521, DOI 10.1007/BF01443609

[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

[ACK] W. Arendt, P. R. Chernoff and T. Kato, A generalization of dissipativity and positive semigroups, J. Operator Theory 8 (1982), 167-180. MR 0670183




[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