Characterizations of Dimension Functions of Wavelet Packets

Abstract

This paper deals with the characterizations of dimension functions of wavelet packets. As a corollary, I prove that if ⍵_n are orthonormal wavelet packets such that |⍵ˆ_n| is continuous and |⍵ˆ_n(ξ)| = O (|ξ|^−1/2−α) at ∞ for some α > 0, then ⍵ˆ_n are MRA wavelet packets.

Key words and phrases. Wavelet packets, multiresolution analysis, dimension function.

2000 Mathematics Subject Classification. 42C15, 41A30, 39B99