On some class of nonseparable continuous wavelet transforms
Almaz Butaev, Ravshan Ashurov · Applicable Analysis · 2011
It is well-known that only a single condition (called the admissibility condition) is sufficient for L 2-convergence of multiple continuous wavelet transforms (MCWT). However known results suggest that to guarantee the pointwise convergence of MCWT for L p -functions wavelets should vanish quite rapidly at infinity. In this article, we consider the class of nonseparable multiple wavelets with square-symmetric Fourier transforms. For these wavelets ψ we prove that the admissibility condition and the condition ψ∈L 1(R n ) are sufficient for the convergence of corresponding MCWT almost everywhere.