论文标题
有界的射击算子和加博尔框架的轨道
Orbits of bounded bijective operators and Gabor frames
论文作者
论文摘要
本文是对框架理论的贡献。希尔伯特空间中的框架是正统基础的概括。特别是，$ l^2（\ Mathbb {r}）$的Gabor帧通常在应用程序中被一个或多个Windows的翻译和调制制成。更确切地说，该论文处理了克里斯滕森（Christensen）和哈纳萨布（Hasannasab）在过去几年中提出的一个问题，内容涉及过时的Gabor框架的存在，有些订购了超过$ \ Mathbb {Z} $，它们是$ l^2（\ Mathbb {r}）$的界限轨道。给出了两类超过的Gabor框架，不能在$ \ mathbb {z} $上订购，并给出了$ gl（l^2（\ Mathbb {r}）$的运算符轨道代表$。关于操作员表示的一些结果在任意框架的一般环境中说明，还涵盖了某些小波框架。
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are often used in applications. More precisely, the paper deals with a question posed in the last years by Christensen and Hasannasab about the existence of overcomplete Gabor frames, with some ordering over $\mathbb{Z}$, which are orbits of bounded operators on $L^2(\mathbb{R})$. Two classes of overcomplete Gabor frames which cannot be ordered over $\mathbb{Z}$ and represented by orbits of operators in $GL(L^2(\mathbb{R}))$ are given. Some results about operator representation are stated in a general context for arbitrary frames, covering also certain wavelet frames.
