Copyright © 2009 Marko Kostić. 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. 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 · View at MathSciNet
2. C. Lizama, “On approximation and representation of $K$-regularized resolvent families,” Integral Equations and Operator Theory, vol. 41, no. 2, pp. 223–229, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
3. C. Lizama and J. Sánchez, “On perturbation of $K$-regularized resolvent families,” Taiwanese Journal of Mathematics, vol. 7, no. 2, pp. 217–227, 2003. View at MathSciNet
4. 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 · View at MathSciNet
5. C. Lizama and H. Prado, “On duality and spectral properties of $(a,k)$-regularized resolvents,” preprint.
6. C. Lizama and V. Poblete, “On multiplicative perturbation of integral resolvent families,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 1335–1359, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
7. M. Li, Q. Zheng, and J. Zhang, “Regularized resolvent families,” Taiwanese Journal of Mathematics, vol. 11, no. 1, pp. 117–133, 2007. View at Zentralblatt MATH · View at MathSciNet
8. I. Ciorănescu and G. Lumer, “Problèmes d'évolution régularisés par un noyau général $K(t)$. Formule de Duhamel, prolongements, théorèmes de génération,” Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, vol. 319, no. 12, pp. 1273–1278, 1994. View at MathSciNet
9. M. Kostić, “Generalized semigroups and cosine functions,” to appear.
10. J. Prüss, Evolutionary Integral Equations and Applications, vol. 87 of Monographs in Mathematics, Birkhäuser, Basel, Switzerland, 1993. View at MathSciNet
11. I. Ciorănescu and G. Lumer, “Regularization of evolution equations via kernels $K(t)$, $K$-evolution operators and convoluted semigroups, generation theorems,” in Seminar Notes in Functional Analysis and PDE, pp. 45–52, Louisiana State Univ., Baton Rouge, La, USA, 1994.
12. 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 · View at MathSciNet
13. M. Kim, Abstract Volterra equations, Ph.D. thesis, Louisiana State University, Baton Rouge, La, USA, 1995.
14. H. Oka, “Linear Volterra equations and integrated solution families,” Semigroup Forum, vol. 53, no. 3, pp. 278–297, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
15. M. Kostić and S. Pilipović, “Convoluted $C$-cosine functions and semigroups. Relations with ultradistribution and hyperfunction sines,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1224–1242, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
16. S. W. Wang and M. C. Gao, “Automatic extensions of local regularized semigroups and local regularized cosine functions,” Proceedings of the American Mathematical Society, vol. 127, no. 6, pp. 1651–1663, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
17. C.-C. Kuo, “A note on weak solutions of second order abstract Cauchy problems,” to appear in Taiwanese Journal of Mathematics.
18. Y.-C. Li and S.-Y. Shaw, “$N$-times integrated $C$-semigroups and the abstract Cauchy problem,” Taiwanese Journal of Mathematics, vol. 1, no. 1, pp. 75–102, 1997. View at MathSciNet
19. V. Keyantuo and M. Warma, “The wave equation in $L^p$-spaces,” Semigroup Forum, vol. 71, no. 1, pp. 73–92, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
20. M. Kim, “Trotter-Kato type approximations of convoluted solution operator families,” Communications of the Korean Mathematical Society, vol. 19, no. 2, pp. 293–305, 2004. View at Zentralblatt MATH · View at MathSciNet
21. C. Müller, “Approximation of local convoluted semigroups,” Journal of Mathematical Analysis and Applications, vol. 269, no. 2, pp. 401–420, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
22. J.-C. Chang and S.-Y. Shaw, “Optimal and non-optimal rates of approximation for integrated semigroups and cosine functions,” Journal of Approximation Theory, vol. 90, no. 2, pp. 200–223, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
23. M. Kim, “Remarks on Volterra equations in Banach spaces,” Communications of the Korean Mathematical Society, vol. 12, no. 4, pp. 1039–1064, 1997. View at Zentralblatt MATH · View at MathSciNet
24. V. Barbu, “Differentiable distribution semi-groups,” Annali dela Scuola Normale Superiore di Pisa, vol. 23, pp. 413–429, 1969. View at Zentralblatt MATH · View at MathSciNet
25. M. Kostić, “Differential and analytical properties of semigroups of linear operators,” preprint.
26. I. Miyadera, M. Okubo, and N. Tanaka, “On integrated semigroups which are not exponentially bounded,” Proceedings of the Japan Academy, Series A, Mathematical Sciences, vol. 69, no. 6, pp. 199–204, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
27. P. C. Kunstmann, “Stationary dense operators and generation of non-dense distribution semigroups,” Journal of Operator Theory, vol. 37, no. 1, pp. 111–120, 1997. View at Zentralblatt MATH · View at MathSciNet
28. B. Bäumer, “Approximate solutions to the abstract Cauchy problem,” in Evolution Equations and Their Applications in Physical and Life Sciences (Bad Herrenalb, 1998), vol. 215 of Lecture Notes in Pure and Appl. Math., pp. 33–41, Marcel Dekker, New York, NY, USA, 2001. View at Zentralblatt MATH · View at MathSciNet
29. E. Bazhlekova, Fractional evolution equations in Banach spaces, Ph.D. thesis, Eindhoven University of Technology, Eindhoven, UK, 2001.
30. R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, vol. 1570 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1994. View at MathSciNet
31. J. Liang, T.-J. Xiao, and F. Li, “Multiplicative perturbations of local $C$-regularized semigroups,” Semigroup Forum, vol. 72, no. 3, pp. 375–386, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
32. Y. Xin and C. Liang, “Multiplicative perturbations of $C$-regularized resolvent families,” Journal of Zheijang University SCIENCE, vol. 5, no. 5, pp. 528–532, 2004.
33. A. Rhandi, “Multiplicative perturbations of linear Volterra equations,” Proceedings of the American Mathematical Society, vol. 119, no. 2, pp. 493–501, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
34. Q. Zheng and Y. Li, “Abstract parabolic systems and regularized semigroups,” Pacific Journal of Mathematics, vol. 182, no. 1, pp. 183–199, 1998. View at Zentralblatt MATH · View at MathSciNet