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Semi-groups of operators


Author: R. S. Phillips
Journal: Bull. Amer. Math. Soc. 61 (1955), 16-33
DOI: https://doi.org/10.1090/S0002-9904-1955-09854-9
MathSciNet review: 0068122
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  • 1. W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math. vol. 55 (1952) pp. 468-519. MR 47886
  • 2. W. Feller, Semi-groups of transformations in general weak topologies, Ann. of Math. vol. 57 (1953) pp. 287-308. MR 54165
  • 3. W. Feller, On the generation of unbounded semi-groups of bounded linear operators, Ann. of Math. vol. 58 (1953) pp. 166-174. MR 55572
  • 4. E. Hille, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publications, vol. 31, New York, 1948. MR 25077
  • 5. E. Hille, On the generation of semi-groups and the theory of conjugate functions, Kungl. Fysiografiska Sällskapets I Lund Förhandlingar vol. 21 (14) (1952) pp. 1-13. MR 45944
  • 6. E. Hille, Le problème abstrait de Cauchy, Università di Torino, Rendiconti del Seminario Mat. vol. 12 (1953) pp. 95-103. MR 60732
  • 7. E. Hille, The abstract Cauchy problem and Cauchy's problem for parabolic differential equations, Journal d'Analyse Mathématiques vol. 3 (1954) pp. 83-196. MR 62934
  • 8. I. Miyadera, Generation of a strongly continuous semi-group of operators, Tôhoku Math. J. vol. 4 (2) (1952) pp. 109-114. MR 52037
  • 9. R. S. Phillips, On one parameter semi-groups of linear transformations, Proc. Amer. Math. Soc. vol. 2 (1951) pp. 234-237. MR 39922
  • 10. R. S. Phillips, Spectral theory for semi-groups of linear operators, Trans. Amer. Math. Soc. vol. 71 (1951) pp. 393-415. MR 44737
  • 11. R. S. Phillips, On the generation of semi-groups of linear operators, Pacific Journal of Mathematics vol. 2 (1952) pp. 343-369. MR 50797
  • 12. R. S. Phillips, Perturbation theory for semi-groups of linear operators, Trans. Amer. Math. Soc. vol. 74 (1953) pp. 199-221. MR 54167
  • 13. R. S. Phillips, An inversion formula for Laplace transforms and semi-groups of linear operators, Ann. of Math. vol. 59 (1954) pp. 325-356. MR 60730
  • 14. R. S. Phillips, A note on the abstract Cauchy problem, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 244-248. MR 61759
  • 15. R. S. Phillips, The adjoint semi-group, to appear in the Pacific Journal of Mathematics.
  • 16. M. H. Stone, Linear transformations in Hilbert space III, Proc. Nat. Acad. Sci. U.S.A. vol. 16 (1930) pp. 172-175.
  • 17. A. E. Taylor, Spectral theory of closed distributive operators, Acta Math. vol. 84 (1950) pp. 189-224. MR 40582
  • 18. D. V. Widder, The Laplace transform, Princeton University Press, 1941. MR 5923
  • 19. K. Yosida, On the differentiability and the representation of one-parameter semigroups of linear operators, J. Math. Soc. of Japan vol. 1 (1948) pp. 15-21. MR 28537
  • 20. K. Yosida, Integration of Fokker-Planck's equation with a boundary condition, J. Math. Soc. of Japan vol. 3 (1951) pp. 69-73. MR 55545
  • 21. K. Yosida, On the integration of diffusion equations in Riemann spaces, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 864-873. MR 52017


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DOI: https://doi.org/10.1090/S0002-9904-1955-09854-9

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