DUALITY THEORY OF REGULARIZED RESOLVENT OPERATOR FAMILY

Jizhou Zhang; Yeping Li

doi:10.11948/2011019

2011 Volume 1 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2011 > 1(2): 279-290

Next Article Previous Article

Jizhou Zhang, Yeping Li. DUALITY THEORY OF REGULARIZED RESOLVENT OPERATOR FAMILY[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 279-290. doi: 10.11948/2011019

Citation:

Jizhou Zhang, Yeping Li. DUALITY THEORY OF REGULARIZED RESOLVENT OPERATOR FAMILY[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 279-290. doi: 10.11948/2011019

DUALITY THEORY OF REGULARIZED RESOLVENT OPERATOR FAMILY

Department of Mathematics, Shanghai Normal University, Shanghai, 200234 China

Fund Project:

Abstract

Abstract

Let k ∈ C(R⁺), A be a closed linear densely defined operator in the Banach space X and {R(t)}_t ≥ 0 be an exponentially bounded k-regularized resolvent operator families generated by A. In this paper, we mainly study pseudo k-resolvent and duality theory of k-regularized resolvent operator families. The conditions that pseudo k-resolvent become k-resolvent of the closed linear densely defined operator A are given. The some relations between the duality of the regularized resolvent operator families and the generator A are gotten. In addition, the corresponding results of duality of k-regularized resolvent operator families in Favard space are educed.
- k-regularized resolvent operator family /
- pseudo k-resolvent /
- duality /
- Favard space
MSC: 47D06;47G10

FullText(HTML)

References

[1]	P. L. Butzer and H. Berens, Semi-Groups of Operators and Approximation, Berlin, Springer-Verlag, 1967. Google Scholar
[2]	P. Clement, O. Diekmann, M. Gyllenberg, H. J. A. M. Heimans and H. R. Thieme, Perturbation theory for dual semigroups I:The sun-reflexive case, Math. Ann., 277(1987), 709-725. Google Scholar
[3]	G. Da Prato and M. Iannelli, Linear integro-differential equation in Banach space, Rend. Sem. Math. Padova, 62(1980), 207-219. Google Scholar
[4]	C. Lizama, Regularized solutions for Volterra equations, J. Math. Anal. Appl., 243(2000), 278-292. Google Scholar
[5]	C. Lizama, A representation formula for strongly continuous resolvent families, J. Integral Equs Appl., 9(1997), 278-292. Google Scholar
[6]	C. Lizama and J. Sánchez. On perturbantion of K-regularized resolvent families, Taiwanese J. Math., 7(2003), 217-227. Google Scholar
[7]	C. Lizama and P. Humberto, On duality and spectral properties of (a, k)-regularized resolvents, Proc. Roy. Soc. Edinburgh, 139A(2009), 505-517. Google Scholar
[8]	M. Jung, Duality theory for solutions to Volterra integral equation, J. Math. Anal. Appl., 230(1999), 112-134. Google Scholar
[9]	A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. Google Scholar
[10]	J. Prüss, Evolutionary Integral Equations anD Applications, Monographs in Mathematics, 87, Birkhaüser Verlag, 1993. Google Scholar