We introduce and study a family of spaces of entire functions in one variable that generalise the classical Paley–Wiener and Bernstein spaces. Namely, we consider entire functions of exponential type a whose restriction to the real line belongs to the homogeneous Sobolev space W˙ s,p and we call these spaces fractional Paley–Wiener if p= 2 and fractional Bernstein spaces if p∈ (1 , ∞) , that we denote by PWas and Bas,p, respectively. For these spaces we provide a Paley–Wiener type characterization, we remark some facts about the sampling problem in the Hilbert setting and prove generalizations of the classical Bernstein and Plancherel–Pólya inequalities. We conclude by discussing a number of open questions.

(2021). Fractional Paley–Wiener and Bernstein spaces [journal article - articolo]. In COLLECTANEA MATHEMATICA. Retrieved from http://hdl.handle.net/10446/202836

Fractional Paley–Wiener and Bernstein spaces

Monguzzi, Alessandro;
2021

Abstract

We introduce and study a family of spaces of entire functions in one variable that generalise the classical Paley–Wiener and Bernstein spaces. Namely, we consider entire functions of exponential type a whose restriction to the real line belongs to the homogeneous Sobolev space W˙ s,p and we call these spaces fractional Paley–Wiener if p= 2 and fractional Bernstein spaces if p∈ (1 , ∞) , that we denote by PWas and Bas,p, respectively. For these spaces we provide a Paley–Wiener type characterization, we remark some facts about the sampling problem in the Hilbert setting and prove generalizations of the classical Bernstein and Plancherel–Pólya inequalities. We conclude by discussing a number of open questions.
articolo
Monguzzi, Alessandro; Peloso, Marco M.; Salvatori, Maura
(2021). Fractional Paley–Wiener and Bernstein spaces [journal article - articolo]. In COLLECTANEA MATHEMATICA. Retrieved from http://hdl.handle.net/10446/202836
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/202836
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