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半直线伸缩调制框架集
The Dilation-and-Modulation Frame Sets on the Half Real Line
本文研究右半直线平方可积函数空间L2（R+）中的一类伸缩调制系.实际问题中时间变量不可取负值，L2（R+）可模拟因果信号空间.但因R+按加法不能作成一个群，它不容许小波与Gabor系.我们研究L2（R+）中由特征函数生成的伸缩调制系（MD-系）框架，引入了R+中MD-框架集的概念，利用"伸缩等价"与"基数函数"方法刻画了L2（R+）中MD-Bessel集与完备集；得到了关于MD-Riesz基集的两个充分条件，并证明了通过对MD-Riesz基集进行有限可测分解可得到MD-框架集.
This paper addresses a class of dilation-and-modulation (MD) systems in the space L2(R+) of square integrable functions defined on the right half real line R+. In practice, the time variable cannot be negative. L2(R+) models the causal signal space, but it admits no wavelet and Gabor systems due to R+ being not a group under addition. We study the dilation-and-modulation systems in L2(R+) generated by characteristic functions. We introduce the notion of MD-frame sets in R+. Using "dilation-equivalence" and "cardinality function" methods we characterize MD-Bessel and complete sets; obtain two sufficient conditions for MD-Riesz basis sets; and prove that an arbitrary finite and measurable decomposition of an MD-Riesz basis set leads to an MD-frame set.
伸缩调制系 / 框架 / Riesz基 {{custom_keyword}} /
dilation-and-modulation system / frame / Riesz basis {{custom_keyword}} /
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国家自然科学基金资助项目（11971043）
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