Applications of an advanced differential equation in the study of wavelets

Abstract A new wavelet family K ( t ) is discussed which represents a natural range of continuous pulse waveforms, deriving from the theory of multiplicatively advanced/delayed differential equations. K satisfies: all moments of K vanish; the Fourier transform of K relates to the Jacobi theta function; and K generates a wavelet frame for L 2 ( R ) . Estimates on the frame bounds as well as the translation parameter are provided.