A unique convergence of new summation method of spherical wavelet expansions of  functions is established in this paper. The SOHO wavelet basis has an effective composition and is considered to be the first spherical wavelet basis that has been recommended for the research of finite energy functions, expanded on the spherical domains and exhibiting almost everywhere convergence. The multiresolution analysis on the spherical domain with its new features is applied to derive a new category of wavelet projection operators on the basis of spherical wavelet expansions on spherical domains that can be utilized to validate the convergence.

SOHO wavelet, convergence, Riesz basis functions, spherical wavelet expansions, partial sum operator.