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

Abstract

We obtain sequence space representations for a class of Fréchet spaces of entire functions with rapid decay on horizontal strips. In particular, we show that the projective Gelfand-Shilov spaces ${\Sigma }_{\nu }^1$ and ${\Sigma }_1^{\nu }$ are isomorphic to ${\Lambda }_{\infty }(n^{1/(\nu +1)})$ for $\nu >0$.

19pages; updated version