Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On Volterra equations associated with a linear operator


Author: Carlos Lizama
Journal: Proc. Amer. Math. Soc. 118 (1993), 1159-1166
MSC: Primary 47N20; Secondary 45D05, 47A50, 47D06, 47G10
DOI: https://doi.org/10.1090/S0002-9939-1993-1152281-3
MathSciNet review: 1152281
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this work we define the Hille-Yosida space, in the sense of S. Kantorovitz, for a Volterra equation of convolution type.


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

  • [1] P. L. Butzer, Die Anwendung des Operatorenkalküls von Jan Mikusinski auf Lineare Integralgleichungen von Faltungstypus, Arch. Rational Mech. Anal. 2 (1958), 114-128. MR 0104112 (21:2874)
  • [2] I. Cioranescu, On the second order Cauchy's problem associated with a linear operator, J. Math. Anal. Appl. (to appear). MR 1087971 (91m:47060)
  • [3] G. Da Prato and M. Ianelli, Linear integrodifferential equations in Banach space, Rend. Sem. Mat. Univ. Padova 62 (1980), 207-219. MR 582951 (82c:45021)
  • [4] R. deLaubenfels and S. Kantorovitz, Laplace and Laplace-Stieltjes space (submitted).
  • [5] H. O. Fattorini, Second order linear differential equations in Banach spaces, North-Holland Math. Stud., vol. 108, North-Holland, Amsterdam, 1985. MR 797071 (87b:34001)
  • [6] R. Grimmer and J. Prüss, On linear Volterra equations in Banach space, Comput. Math. Appl., vol. 11, Pergamon Press, New York, 1985, pp. 189-205. MR 787436 (86h:45004)
  • [7] H. Henriquez and E. Hernandez, On the abstract Cauchy problem in Fréchet spaces, Proc. Amer. Math. Soc., 115 (1992), 353-360. MR 1081092 (92i:47043)
  • [8] E. Hille and R. Phillips, Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, RI, 1957. MR 0089373 (19:664d)
  • [9] S. Kantorovitz, The Hille-Yosida space of an arbitrary operator, J. Math. Anal. Appl. 136 (1988), 107-111. MR 972586 (90a:47097)
  • [10] S. G. Krein, G I. Laptev, and G A. Cretkova, On Hadamard correctness of the Cauchy problem for the equation of evolution, Soviet Math. Dokl. 11 (1970), 763-766.
  • [11] C. Lizama, On an extension of the Trotter-Kato theorem for resolvent families of operators, J. Integral Equations Appl. 2 (1990), 269-280. MR 1045773 (91c:47093)
  • [12] -, A characterization of periodic resolvent operators, Results in Math. 18 (1990), 93-105. MR 1066645 (91j:47045)
  • [13] -, Uniform continuity and compactness of resolvent families of operators (submitted).
  • [14] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer, Berlin, Heidelberg, New York, and Tokyo, 1983. MR 710486 (85g:47061)
  • [15] J. Prüss, Positivity and regularity of hyperbolic Volterra equations in Banach spaces, Math. Ann. 279 (1987), 317-344. MR 919509 (89h:45004)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47N20, 45D05, 47A50, 47D06, 47G10

Retrieve articles in all journals with MSC: 47N20, 45D05, 47A50, 47D06, 47G10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1152281-3
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society