论文标题
分数佩奇和伯恩斯坦空间
Fractional Paley-Wiener and Bernstein spaces
论文作者
论文摘要
我们在一个变量中介绍并研究了整个功能的一系列空间家族，该变量概括了经典的Paley-Wiener和Bernstein空间。即，我们考虑了指数类型$ a $的全部功能，其对实际线的限制属于同质的sobolev space $ \ dot {w}^{s，p} $，我们称这些空间为分数的paley-wiener，如果$ p = 2 $ and nif $ p = $ p \ in（$ pw），则$ p \ in（1，$ pw） $ \ Mathcal b^{s，p} _a $。对于这些空间，我们提供了佩奇的类型特征，我们指出了有关希尔伯特环境中抽样问题的一些事实，并证明了古典伯恩斯坦和Plancherel-Pólya不平等现象的概括。我们通过讨论许多开放问题来结束。
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. 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.
