p-Wavelet frame packets on a half-line using the Walsh–Fourier transform

Abstract

This paper deals with a construction of wavelet frame packets on the positive half-line ℝ⁺ using the splitting trick for frames. It is shown that, as long as finitely many splitting steps are applied, the resulting sequence of functions is a frame of L ²(ℝ⁺). If the matrix M(ξ) associated with the splitting is unitary, then the splitting can be applied infinitely many times to prove the existence of frame with the frame bounds as shown in Theorem 3.3.

Keywords:

• orthogonal p-wavelets
• frames
• p-wavelet packets
• Walsh–Fourier transform

2000 AMS Mathematics Subject Classification :

• 42C15
• 42C40
• 42C10
• 42A38