2021/10/07 by Nikolay Kuznetsov, Kuznetsov, Nikolay
Mathematics · Computer Science · #Numerical methods in inverse problems #Algebraic and Geometric Analysis #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2110.03449
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation (panharmonic functions) is given. Another description of harmonic functions is the pointwise equality of a function and its iterated mean over an admissible pair of spheres.