About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 683021, 14 pages
http://dx.doi.org/10.1155/2012/683021
Research Article

The Maximal Subspace for Generation of -Regularized Families

1Facultad de Ciencias Básicas, Universidad Tecnológica de Bolívar, Cartagena, Colombia
2Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

Received 25 May 2012; Revised 7 September 2012; Accepted 12 September 2012

Academic Editor: Patricia J. Y. Wong

Copyright © 2012 Edgardo Alvarez-Pardo and Carlos Lizama. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Kantorovitz, “The Hille-Yosida space of an arbitrary operator,” Journal of Mathematical Analysis and Applications, vol. 136, no. 1, pp. 107–111, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. I. Cioranescu, “On the second order Cauchy problem associated with a linear operator,” Journal of Mathematical Analysis and Applications, vol. 154, no. 1, pp. 238–242, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. C. Lizama, “On volterra equations associated with a linear operator,” Proceedings of the American Mathematical Society, vol. 118, no. 4, pp. 1159–1166, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. G. Da Prato and M. Iannelli, “Linear integro-differential equations in Banach spaces,” Rendiconti del Seminario Matematico dell'Università di Padova, vol. 62, pp. 207–219, 1980. View at Zentralblatt MATH
  5. W. Arendt, C. J. K. Batty, M. Hieber, and F. Neubrander, Vector-Valued Laplace Transforms and Cauchy Problems, vol. 96 of Monographs in Mathematics, Birkhäuser, Basel, Switzerland, 2001. View at Zentralblatt MATH
  6. C. Lizama, “Regularized solutions for abstract Volterra equations,” Journal of Mathematical Analysis and Applications, vol. 243, no. 2, pp. 278–292, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. M. Kostic, “(a,k)—regularized C-resolvent families: regularity and local properties,” Abstract and Applied Analysis, vol. 2009, Article ID 858242, 27 pages, 2009. View at Publisher · View at Google Scholar
  8. C. Lizama and P. J. Miana, “A Landau-Kolmogorov inequality for generators of families of bounded operators,” Journal of Mathematical Analysis and Applications, vol. 371, no. 2, pp. 614–623, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. C. Lizama and J. Sánchez, “On perturbation of K—regularized resolvent families,” Taiwanese Journal of Mathematics, vol. 7, no. 2, pp. 217–227, 2003.
  10. C. Lizama and H. Prado, “On duality and spectral properties of (a,k)—regularized resolvents,” Proceedings of the Royal Society of Edinburgh A, vol. 139, no. 3, pp. 505–517, 2009. View at Publisher · View at Google Scholar
  11. C. Lizama and H. Prado, “Rates of approximation and ergodic limits of regularized operator families,” Journal of Approximation Theory, vol. 122, no. 1, pp. 42–61, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. S.-Y. Shaw and J.-C. Chen, “Asymptotic behavior of (a,k)-regularized resolvent families at zero,” Taiwanese Journal of Mathematics, vol. 10, no. 2, pp. 531–542, 2006.
  13. S.-Y. Shaw and H. Liu, “Continuity of restrictions of (a,k)—regularized resolvent families to invariant subspaces,” Taiwanese Journal of Mathematics, vol. 13, no. 2A, pp. 535–544, 2009.
  14. M. Kostić, Generalized Semigroups and Cosine Functions, vol. 23 of Posebna Izdanja, Matematički Institut SANU, Belgrade, 2011.
  15. C. Lizama and G. M. N'Guérékata, “Bounded mild solutions for semilinear integro differential equations in Banach spaces,” Integral Equations and Operator Theory, vol. 68, no. 2, pp. 207–227, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. H. Kellerman and M. Hieber, “Integrated semigroups,” Journal of Functional Analysis, vol. 84, no. 1, pp. 160–180, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. W. Arendt and H. Kellerman, Integrated Solutions of Volterra Integrodifferential Equations and Applications, vol. 190 of Pitman Research Notes in Mathematical, 1987.
  18. R. Gorenflo and F. Mainardi, “Fractional calculus: integral and differential equations of fractional order,” in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. MainardiParaaaa, Eds., pp. 223–276, Springer, New York, NY, USA, 1997.
  19. F. Mainardi and R. Gorenflo, “On Mittag-Leffler-type functions in fractional evolution processes,” Journal of Computational and Applied Mathematics, vol. 118, no. 1-2, pp. 283–299, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. R. Gorenflo and F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Order, Fractals and Fractional Calculus in Continuum Mechanics, Springer, New York, NY, USA, 1997.
  21. H. J. Haubold, A. M. Mathai, and R. K. Saxena, “Mittag-Leffler functions and their applications,” Journal of Applied Mathematics, vol. 2011, Article ID 298628, 51 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. C. Chen, M. Li, and F.-B. Li, “On boundary values of fractional resolvent families,” Journal of Mathematical Analysis and Applications, vol. 384, no. 2, pp. 453–467, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Elsevier, 2007.