Sequence space representations for spaces of entire functions with rapid decay on strips

We obtain sequence space representations for a class of Frechet spaces of entire functions with rapid decay on horizontal strips. In particular, we show that the projective Gelfand-Shilov spaces $Sigma^1_ u$ and $Sigma^ u_1$ are isomorphic to $Lambda_{infty}(n^{1/( u+1)})$ for $ u > 0$.