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- W3007028305 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 $dot{W}^{s,p}$ and we call these spaces fractional Paley-Wiener if $p=2$ and fractional Bernstein spaces if $pin(1,infty)$, that we denote by $PW^s_a$ and $mathcal B^{s,p}_a$, 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-Polya inequalities. We conclude by discussing a number of open questions." @default.
- W3007028305 created "2020-03-06" @default.
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- W3007028305 date "2020-02-27" @default.
- W3007028305 modified "2023-09-23" @default.
- W3007028305 title "Fractional Paley-Wiener and Bernstein spaces" @default.
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