# TROTTER-KATO TYPE APPROXIMATIONS OF CONVOLUTED SOLUTION OPERATOR FAMILIES

• Kim, Mi-Hi (Department of Mathematics Kyung Hee University)
• Published : 2004.04.01
• 80 20

#### Abstract

Trotter-Kato type approximations of the convoluted solution operator families for the Volterra integral equations (V $E_n$): v(t)=$A_{n} \int_0^t v(t-s) d\mu_n(s) + f_n(t), t \geq 0$ and the convergence of the solutions to the equations (V $E_n$) are studied.

#### Keywords

convoluted solution operator family;integrated solution operator family;Laplace transform;Trotter-Kato type approximation;Volterra equation

#### References

1. Commun. Korean Math. Soc. v.12 no.4 Remarks on Volterra equations in Banach spaces
2. J. Math. Anal. Appl. v.180 The Hille-Yosida and Trotter-Kato theorems for integrated semi groups S.Nicaise https://doi.org/10.1006/jmaa.1993.1402
3. SIAM J. Math. Anal. v.20 Small structured population models and the Trotter-Kato theorem H.J.A.M.Heijmans;J.A.J.Metz https://doi.org/10.1137/0520059
4. Abstract Volterra equations,Dissertation M.Kim
5. Appl. Anal. v.49 On representations,inversions, and approximations of Laplace transforms in Banach spaces B.Hennig;F.Neubrander https://doi.org/10.1080/00036819108840171
6. Conf. Semin. Mat. v.259 Laplace transform methods for evolution equations B.Baumer;F.Neubrander
7. J. Math. Anal. Appl. v.181 On the convergence and approximation of integrated semigroups C.Lizama https://doi.org/10.1006/jmaa.1994.1007

#### Cited by

1. Abstract Volterra equations in locally convex spaces vol.55, pp.9, 2012, https://doi.org/10.1007/s11425-012-4477-9
2. (a,k)-RegularizedC-Resolvent Families: Regularity and Local Properties vol.2009, 2009, https://doi.org/10.1155/2009/858242