Generalization of two-dimensional radial wavelets

The paper is devoted to the generalization of two-dimensional radial wavelets. Direct and inverse integral wavelet transforms are constructed by means of elliptically symmetric wavelets. Theorems on the relation between functions and their integral wavelet transforms, on the convergence of the integral wavelet transform in $L^2(\mathbb R^2)$, and on the pointwise convergence of the inverse integral wavelet transform are proved.