Enhanced Symmetry of the $p$-adic Wavelets

Understand

Wavelet analysis has been extended to the $p$-adic line $\mathbb{Q}_p$.

• The $p$-adic wavelets are complex valued functions with compact support.
• As in the case of real wavelets, the construction of the basis functions is recursive, employing scaling and translation.
• Consequently, wavelets form a representation of the affine group generated by scaling and translation.