Construction of Pth-Stage Nonuniform Discrete Wavelet Frames

Motivated by the work of Frazier; and Gabardo and Nashed, we study P-th-stage nonuniform discrete wavelet frames (P-th-stage NUDW frames, in short) for l(2) (Lambda), a nonuniform discrete space. In nonuniform discrete wavelet frames, the translation set is not necessary a group but a spectrum which is based on the theory of spectral pairs. We characterize first-stage nonuniform discrete Bessel sequences and wavelet frames in nonuniform discrete spaces. Duality and stability of first-stage NUDW frames are also discussed. Finally, by using first-stage NUDW frames, we provide a suitable way to construct the P-th-stage NUDW frames. We illustrate our construction with the help of a concrete example.