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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 683021, 14 pages
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.
- S. Kantorovitz, “The Hille-Yosida space of an arbitrary operator,” Journal of Mathematical Analysis and Applications, vol. 136, no. 1, pp. 107–111, 1988.
- 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.
- C. Lizama, “On volterra equations associated with a linear operator,” Proceedings of the American Mathematical Society, vol. 118, no. 4, pp. 1159–1166, 1993.
- 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.
- 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.
- C. Lizama, “Regularized solutions for abstract Volterra equations,” Journal of Mathematical Analysis and Applications, vol. 243, no. 2, pp. 278–292, 2000.
- M. Kostic, “—regularized C-resolvent families: regularity and local properties,” Abstract and Applied Analysis, vol. 2009, Article ID 858242, 27 pages, 2009.
- 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.
- C. Lizama and J. Sánchez, “On perturbation of —regularized resolvent families,” Taiwanese Journal of Mathematics, vol. 7, no. 2, pp. 217–227, 2003.
- C. Lizama and H. Prado, “On duality and spectral properties of —regularized resolvents,” Proceedings of the Royal Society of Edinburgh A, vol. 139, no. 3, pp. 505–517, 2009.
- 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.
- S.-Y. Shaw and J.-C. Chen, “Asymptotic behavior of -regularized resolvent families at zero,” Taiwanese Journal of Mathematics, vol. 10, no. 2, pp. 531–542, 2006.
- S.-Y. Shaw and H. Liu, “Continuity of restrictions of —regularized resolvent families to invariant subspaces,” Taiwanese Journal of Mathematics, vol. 13, no. 2A, pp. 535–544, 2009.
- M. Kostić, Generalized Semigroups and Cosine Functions, vol. 23 of Posebna Izdanja, Matematički Institut SANU, Belgrade, 2011.
- 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.
- H. Kellerman and M. Hieber, “Integrated semigroups,” Journal of Functional Analysis, vol. 84, no. 1, pp. 160–180, 1989.
- W. Arendt and H. Kellerman, Integrated Solutions of Volterra Integrodifferential Equations and Applications, vol. 190 of Pitman Research Notes in Mathematical, 1987.
- 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.
- 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.
- 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.
- 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.
- 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.
- I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Elsevier, 2007.