A Gevrey space characterization of certain Gelfand-Shilov spaces Sαβ

Abstract

Let p,q ∈ ℕ and let ϱ≥ϱ_p,q with ϱ_p,q = max {l/p, l/q}, ϱ_p1, = 1/p, and ϱ_1,q= 1/q, p,q>l. In this paper it is proved that there exist symmetric differential operators A_p,q in L₂(ℝ) such that the Gelfand-Shilov space S_pϱ^pϱ is equal to the Gevrey space of order 2pqϱ relative to A_p,q.