局部域及相关群的小波理论
A wavelet theory for local fields and related groups
摘要：
设G是局部紧阿贝尔群，其紧开子群H.这样一个群最著名的例子是G=Q_p，p进有理数域（作为加法下的群），它有紧开子群H=Z_p，p进整数环。经典的小波理论，这需要一个非平凡的离散子群的翻译，不适用于G，它可能没有这样的子群。利用G的对偶群的商的陪集表示，发展了G上的小波理论。小波基的构造是通过一种迭代法，在对偶群中产生所谓的小波集。
英文摘要：
Let G be a locally compact abelian group with compact open subgroup H. The best known example of such a group is G=Q_p, the field of p-adic rational numbers (as a group under addition), which has compact open subgroup H=Z_p, the ring of p-adic integers. Classical wavelet theories, which require a non-trivial discrete subgroup for translations, do not apply to G, which may not have such a subgroup. A wavelet theory is developed on G using coset representatives of a quotient of the dual group of G. Wavelet bases are constructed by means of an iterative method giving rise to so-called wavelet sets in the dual group.
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。
