# Fractional Paley-Wiener and Bernstein spaces

17 Mar 2020 Monguzzi Alessandro Peloso Marco M. Salvatori Maura

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 $p\in(1,\infty)$, that we denote by $PW^s_a$ and $\mathcal B^{s,p}_a$, respectively... (read more)

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# Categories

• COMPLEX VARIABLES
• FUNCTIONAL ANALYSIS