Some Localization Properties of the L^p Continuous Wavelet Transform

ABSTRACT

We shall prove some simultaneous localization or concentration inequalities for the continuous wavelet transform. We will also show that simultaneous localization in the scale-time(space) is impossible, in the sense that the scale sections of the support of wavelet transform of a nonnull L^p-function can not have finite Lebesgue measure. Finally, some properties of the support of continuous wavelet transform of band-limited functions are studied.

KEYWORDS:

• Continuous wavelet transform
• uncertainty principles
• L^p spaces

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 42C40
• 26D15
• 42A99
• 42C99