Continuous wavelet transform and uncertainty principle related to the Weinstein operator

ABSTRACT

In this paper, we define and study the continuous wavelet transform $T_{\psi }$ associated with the Weinstein operator. Next, we analyse the concentration of this transform on sets of finite measure. We also establish an analogue of Heisenberg's inequality for wavelet transform. Last, we prove a quantitative version of Shapiro's mean dispersion theorem for the continuous wavelet transform.

KEYWORDS:

• Weinstein operator
• admissible wavelet
• wavelet transform
• uncertainty principles

AMS CLASSIFICATION:

• 42B10
• 42C40
• 43A32

Disclosure statement

No potential conflict of interest was reported by the authors.