The spherical linear canonical transform: Definition and properties

The spherical Fourier transform has attracted considerable attention in the fields of acoustics, optics, and heat because of its superiority in solving practical problems- within the confines of spherical symmetry. A spherical linear canonical transform in spherical polar coordinates is investigated in this study. First, definitions of the spherical linear canonical transform and spherical linear canonical Hankel transform are proposed. Second, the relationship between the spherical linear canonical transform and spherical linear canonical Hankel transform is derived based on the orthogonality of the spherical harmonics. Finally, several essential properties of the proposed spherical linear canonical transform were obtained based on this relationship, including linearity, inversion formulas, shifts, and convolution theorems. Finally, potential applications of the spherical linear canonical transform are discussed.