论文标题
功率扩张系统$ \ {f（z^k）\} _ {k \ in \ mathbb {n}} $ in dirichlet-type spaces
Power dilation systems $\{f(z^k)\}_{k\in\mathbb{N}}$ in Dirichlet-type spaces
论文作者
论文摘要
在本文中，我们专注于功率扩张系统$ \ {f（z^k）\} _ {k \ in \ mathbb {n}} $ in Dirichlet-type spaces $ \ mathcal {d} _t} _t _t \（t \ in \ mathbb {r}）$。当$ t \ neq0 $时，我们证明$ \ {f（z^k）\} _ {k \ in \ mathbb {n}} $在$ \ mathcal {d} _t $中是正交的，仅当$ f = cz^n $对于某些常数$ c $且某些阳性integer $ n $ n $ f = cz^n $，并且仅当一些正面的inte inte $ n $。我们还提供了由Drichlet型空间的功率扩张系统形成的无条件基础和帧的完整表征。
In this paper, we concentrate on power dilation systems $\{f(z^k)\}_{k\in\mathbb{N}}$ in Dirichlet-type spaces $\mathcal{D}_t\ (t\in\mathbb{R})$. When $t\neq0$, we prove that $\{f(z^k)\}_{k\in\mathbb{N}}$ is orthogonal in $\mathcal{D}_t$ only if $f=cz^N$ for some constant $c$ and some positive integer $N$. We also give complete characterizations of unconditional bases and frames formed by power dilation systems for Drichlet-type spaces.
