Abstract
In this paper we have considered composition operators on the several variable Paley-Wiener space Lπ2(Cn). We have proved that for any continuous function ϕ:Cn→Cn the composition operator Cϕ on Lπ2(Cn) is bounded iff ϕ has the following form:ϕ(z)=Az+b,z∈Cn, where A∈GL(n,R) with ||A||op≤1 and b∈Cn. Our proof is different from the single variable case and mainly depends on a theorem of Malgrange, some techniques from harmonic analysis and certain asymptotic behaviour of Bessel's function.
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