Name
Abstract | ||
|---|---|---|
The preservation of stability under the convolution is shown to be related with the zero set of the Fourier transform of inducing stable function. For example, let φ be in the class Λ0 of all stable functions ψ such that
<img src="/fulltext-image.asp?format=htmlnonpaginated&src=P0L14351674T7338_html\10444_2004_Article_5110590_TeX2GIFIE1.gif" border="0" alt="
$$\widehat\psi \left( 0 \right) \ne 0{\text{ and }}\widehat\psi$$
" /> as well as
<img src="/fulltext-image.asp?format=htmlnonpaginated&src=P0L14351674T7338_html\10444_2004_Article_5110590_TeX2GIFIE2.gif" border="0" alt="
$$E_\psi : = \sum {\left| {\widehat\psi \left( {w + 2{\pi }k} \right)} \right|} ^2$$
" /> is continuous. Then Λ0 is preserved under the convolution by φ if and only if the zero set
<img src="/fulltext-image.asp?format=htmlnonpaginated&src=P0L14351674T7338_html\10444_2004_Article_5110590_TeX2GIFIE3.gif" border="0" alt="
$$Z\left( {\widehat\varphi } \right)$$
" /> is contained in 2πZ\{0}. The condition can be transformed into the zero set of the inducing mask trigonometric polynomial in the class Λ# of compactly supported refinable functions in Λ0. For example, our result shows that such φ must have its mask of the form |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1023/A:1022811229621 | Adv. Comput. Math. |
Keywords | DocType | Volume |
stable,refinable,mask,convolution,MRA | Journal | 19 |
Issue | ISSN | Citations |
1-3 | 1572-9044 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gee Ju Chae | 1 | 1 | 0.82 |
| Hong Oh Kim | 2 | 0 | 0.34 |