Continuity of Nonseparable Quincunx Wavelets

Autor: Villemoes, Lars F.
Zdroj: Applied and Computational Harmonic Analysis; March 1994, Vol. 1 Issue: 2 p180-187, 8p
Abstrakt: We characterize the continuous compactly supported solutions to the bidimensional refinement equation where the dilation matrix corresponds to a multiplication by √2 followed by a rotation of π/4. The exact Hölder exponent is found in terms of the spectral radius of an operator acting on a subspace of ℓ1(Z2). The corresponding wavelet basis is generated by a single function ψ, and the existence of such an orthonormal basis for L2(R2), where ψ is continuous and compactly supported, follows from estimates of the above spectral radius.
Databáze: Supplemental Index