Composition operators on spaces of entire functions

Abstract

Abstract. In this paper we study composition operators on spaces of entire functions. We determine which entire functions induce bounded composition operators on the Paley-Wiener space, L 2 π , and on the E 2 (γ) spaces. In addition, we characterize compact composition operators on these spaces. We also study the cyclic properties of composition operators acting on L 2 π .

Composition operators on Hilbert spaces of entire functions

“…We obtain criteria for boundedness and compactness of composition operators on these classes. In particular, we generalized the corresponding results of [1] even to the cases when the condition…”

“…Following these results, the authors of [1] defined composition operators C ϕ acting on the spaces E 2 γ with (n+1)γ n+1 γ n ↓ τ > 0, and derived the criteria for boundedness and compactness of these operators.…”

“…Be reminded that the condition β ∈ G is the main assumption in the paper [1], but G is rather small: it is contained even in the intersection A ∩ B ∩ C ∩ D ∩ E.…”

“…The paper [1] only dealt with problems of composition operators on the smallest class of spaces E 2 γ (T , τ ). In the next section, we study these problems for larger classes of Hilbert spaces of entire functions, namely {H(β, ρ + )} and {H(β, ρ + , T )}.…”

“…For any space E 2 γ (T , τ ), i.e. a space H(β, E) with β ∈ G, the criteria for the boundedness and compactness of C ϕ have been discovered in [1]. It should be noted that with the techniques of [1], one cannot remove the assumption μ(n) ↓ τ > 0.…”