Integral Equations and Operator Theory

, Volume 4, Issue 3, pp 311–329 | Cite as

Some aspects of E. Hille's contribution to semi-group theory

  • Kôsaku Yosida


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  1. Balakrishnan, V. [1] Fractional powers of closed operators and the semigroup generated by them, Pacific J. of Math.,10 (1960), 419–437.Google Scholar
  2. Bochners, S. [1] Diffusion equations and stochastic processes, Proc. Nat. Acad. Sci. U.S.A.,35 (1949), 369–370.Google Scholar
  3. Dunford, N.-Segal, I.E. [1] Semi-groups of operators and the Weierstrass theorem, Bull. Amer. Math. Soc.,52 (1946), 911–914.Google Scholar
  4. Feller, W. [1] The parabolic differential equation and the associated semi-group of transformations, Ann. of Math.,55 (1952), 468–519.Google Scholar
  5. [2] On the generation of unbounded semi-groups of bounded linear operators, Ann. of Math.,58 (1953), 166–174.Google Scholar
  6. Hille, E. [1] Functional Analysis and Semi-groups, Amer. Math. Soc., 1948 (to be referred to as the first edition).Google Scholar
  7. [2] Notes on linear transformations, I, Trans. Amer. Math. Soc.,39, No. 1 (1936), 131–153.Google Scholar
  8. [3] On semi-groups of transformations in Hilbert spaces, Proc. Nat. Acad. Sci. U.S.A.,24, No. 3 (1938), 159–161.Google Scholar
  9. [4] Notes on linear transformations, II, Analyticity of semi-groups, Ann. of Math.,40, No. 1 (1939), 1–47.Google Scholar
  10. [5] Representation of one-parameter semi-groups of linear transformations, Proc. Nat. Acad. Sci. U.S.A.,38, No. 5 (1942), 175–178.Google Scholar
  11. [6] (with Phillips, R. S.): Functional Analysis and Semi-groups, Amer. Math. Soc., Revised edition (1957) (to be referred to as the second edition).Google Scholar
  12. [7] On the differentiability of semi-group operators, Acta Sci. Math. Szeged,12B (1950), 89–114.Google Scholar
  13. [8] On the integration problem for Fokker-Planck's equation in the theory of stochastic processes, C. R. Onzième Cong. Math. Scand. Trondheim, (1949), 183–194.Google Scholar
  14. [9] Some aspect of Cauchy's problem, Proc. Internat. Cong. of Mathematicians, (1954), Amsterdam.Google Scholar
  15. [10] The abstract Cauchy's problem and Cauchy's problem for parabolic equations, J. d'Analyse Math.,3 (1954), 81–196.Google Scholar
  16. [11] "Explosive" solutions of Fokker-Planck's equation, Proc. Internat. Cong. of Mathematicians, (1950), Cambridge, Vol.I, 453.Google Scholar
  17. [12] Une généralization du problème du Cauchy, Ann. Inst. Fourier,4 (1952), 31–48.Google Scholar
  18. Hirsch, F. [1] Familles résolvents, générateurs, cogénérateurs, potentiels, Ann. Inst. Fourier,22 (1972), 89–210.Google Scholar
  19. Kato. T. [1] Integration of the equation of evolution in a Banach space, J. Math. Soc. Japan,5 (1953), 208–234.Google Scholar
  20. [2] Perturbation Theory of Linear Operators, Springer-Verlag (1980), Corrected Printing of the 2nd edit.Google Scholar
  21. [3] Linear evolution equations of hyperbolic type, J. Fac. Sci. Univ. Tokyo, Sect. 1,17 (1970), 241–253.Google Scholar
  22. Krein, S. [1] Linear Differential Equations in Banach Spaces, Amer. Math. Soc., (1971).Google Scholar
  23. Lax, P. [1] Abstract 180, Bull. Amer. Math. Soc.,58 (1952), 192.Google Scholar
  24. Miyadera, I. [1] Generation of a strongly continuous semi-group of operators, Tohoku Math. J.,4 (1952), 109–114.Google Scholar
  25. Phillips, R. S. [1] Perturbation theory for semi-groups of linear operators, Trans. Amer. Math. Soc.,74 (1953), 199–221.Google Scholar
  26. [2] On the generation of semi-groups of linear operators, Pacific J. of Math.,2 (1952), 343–369.Google Scholar
  27. Sobolevski, P. E. [1] Parabolic type equations in Banach spaces, Trudy Moscow Math.,10 (1961), 297–350.Google Scholar
  28. Tanabe, H. [1] On the equations of evolution in a Banach space, Oska Math. J.,12 (1960), 365–613.Google Scholar
  29. Yosida, K. [1] On the differentiability and the representation of one-parameter semi-groups of linear operators, J. Math. Soc. Japan,1 (1948), 15–21.Google Scholar
  30. [2] An operator-theoretical treatment of temporally homogeneous Markoff processes, J. Math. Soc. Japan,1 (1949), 244–253.Google Scholar
  31. [3] Functional Analysis, 6th edition, Springer-Verlag (1980).Google Scholar
  32. [4] Time dependent evolution equations in a locally convex space, Math. Zeitschr.162 (1965), 83–86.Google Scholar
  33. [5] The existence of the potential operator associated with an equi-continuous semi-group of class (C0), Studia Math.,31 (1968), 531–533.Google Scholar

Copyright information

© Birkhäuser Verlag 1981

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.University of TokyoJapan

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