  Continuous wavelet design is the endeavor to construct mother wavelets with
desirable properties for the continuous wavelet transform (CWT). One class of
methods for choosing a mother wavelet involves minimizing a functional, called
the wavelet uncertainty functional. Recently, two new wavelet uncertainty
functionals were derived from theoretical foundations. In both approaches, the
uncertainty of a mother wavelet describes its concentration, or accuracy, as a
time-scale probe. While an uncertainty minimizing mother wavelet can be proven
to have desirable localization properties, the existence of such a minimizer
was never studied. In this paper, we prove the existence of minimizers for the
two uncertainty functionals.
