威爾森展開式之充要條件

王昆湶

慈濟技術學院醫務管理系

摘　要

　　 延續對小波展開式與蓋柏展開式的充要條件之探討，我們對威爾森展開式的充要條件作一完整的研究。不似小波展開式，其允許非正交的展開式，在威爾森展開式的情況下，當適當的條件給定後，必是一個正交的展開式。

關鍵字：小波展開式、蓋柏展開式、威爾森展開式、正交基底。



Necessary and Sufficient Conditions
for Expansions of Wilson Type
Kunchuan Wang

Department of Health Administration

Tzu-Chi College of Technology

Abstract
　We characterize the expansions of the type arising from Wilson bases. As an application, we see that such an expansion must be orthonormal, in contract to the case of wavelet expansions generated by translations and dilations. In the Wilson case, there are no “fake” orthonormal expansions. Note that the corresponding result is fake for standard wavelet-type expansions, even with since the -transform yields an example when for all , but are not orthonormal.

Key Words: wavelet expansion, Gabor expansion, Wilson expansion, and orthonormal basis.