Bull. Korean Math. Soc. 2007 Vol. 44, No. 3, 419-428 Printed September 1, 2007

Dennis Nemzer California State University

Abstract : The space of periodic Boehmians with $\Delta$--convergence is a complete topological algebra which is not locally convex. A family of Boehmians $\{T_\lambda\}$ such that $T_0$ is the identity and $T_{\lambda_1 + \lambda_2} = T_{\lambda_1} \ast T_{\lambda_2}$ for all real numbers $\lambda_1$ and $\lambda_2$ is called a one-parameter group of Boehmians. We show that if $\{T_\lambda\}$ is strongly continuous at zero, then $\{T_\lambda\}$ has an exponential representation. We also obtain some results concerning the infinitesimal generator for $\{T_\lambda\}$.