Schwartz调和分布的连续小波变换

IF 0.1 Q4 MATHEMATICS Cogent mathematics & statistics Pub Date : 2019-01-01 DOI:10.1080/25742558.2019.1623647
J. Pandey, S. K. Upadhyay
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引用次数: 2

摘要

摘要研究了Schwartz调和分布的连续小波变换,并导出了相应的小波逆变换公式(常调和分布的有效模)。但是,本小波反演公式的唯一性定理对于通过从空间中过滤(删除)(i)所有非零常数分布,(ii)所有以分布为并集出现的非零常数而获得的空间是有效的。例如,在考虑分布时,我们将省略1,只保留1。确定小波变换所考虑的小波核是那些所有矩都为非零的小波。举个例子,就是这样一个小波。是一个任意常数。存在许多其他类别的此类小波。在我们的分析中,我们不使用任何矩为零的小波核。
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Continuous wavelet transform of Schwartz tempered distributions
Abstract The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in . But uniqueness theorem for the present wavelet inversion formula is valid for the space obtained by filtering (deleting) (i) all non-zero constant distributions from the space , (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution we would omit 1 and retain only . The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, is such a wavelet. is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.
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