Existence of uncertainty minimizers for the continuous wavelet transform

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