### Automorphisms and derivations of a Fréchet algebra of locally integrable functions

We find representations for the automorphisms, derivations and multipliers of the Fréchet algebra $L{\xb9}_{loc}$ of locally integrable functions on the half-line ${\mathbb{R}}^{+}$. We show, among other things, that every automorphism θ of $L{\xb9}_{loc}$ is of the form $\theta ={\phi}_{a}{e}^{\lambda X}{e}^{D}$, where D is a derivation, X is the operator of multiplication by coordinate, λ is a complex number, a > 0, and ${\phi}_{a}$ is the dilation operator $\left({\phi}_{a}f\right)\left(x\right)=af\left(ax\right)$ ($f\in L{\xb9}_{loc}$, $x\in {\mathbb{R}}^{+}$). It is also shown that the automorphism group is a topological group with the topology of uniform convergence on bounded...