投影与并元Parseval框架MRA小波
Projections and Dyadic Parseval Frame MRA Wavelets
摘要：
奈马克的一个经典定理指出，给定希尔伯特空间$\mathcal{H}$中的Parseval框架$\mathcal{B}$，可以将$\mathcal{H}$嵌入更大的希尔伯特空间$\mathcal{K}$中，使得$\mathcal{B}$的图像是$\mathcal{K}$的规范正交基的投影。在目前的工作中，我们重新审视的概念Parseval框架MRA小波从两篇论文的Paluszyovski，Šikić，Weiss，和肖（PSWX），并产生一个模拟Naimark的定理，这些小波在其尺度函数的水平。我们的目标是使这个讨论尽可能独立，并提供一个不同的观点Parseval框架MRA小波比PSWX。
英文摘要：
A classical theorem attributed to Naimark states that, given a Parseval frame $\mathcal{B}$ in a Hilbert space $\mathcal{H}$, one can embed $\mathcal{H}$ in a larger Hilbert space $\mathcal{K}$ so that the image of $\mathcal{B}$ is the projection of an orthonormal basis for $\mathcal{K}$. In the present work, we revisit the notion of Parseval frame MRA wavelets from two papers of Paluszyński, Šikić, Weiss, and Xiao (PSWX) and produce an analog of Naimark's theorem for these wavelets at the level of their scaling functions. We aim to make this discussion as self-contained as possible and provide a different point of view on Parseval frame MRA wavelets than that of PSWX.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
