ABSTRACT
According to this proposition a wavelet has mean value 0. Prom this we infer that the graph 0(φ) of a wavelet φ lies, as most graphs of “waves” do, partly above and partly below the t-axis.
Γ A function φ of the described kind is automatically in L1, and one has
By (2.9) the Fourier transform ip is continuous. Then the integral (2) can only converge if ψ(0) = 0 .
