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math.AP2021
Harmonicity of a function via harmonicity of its spherical means
Nikolay Kuznetsov
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 characterizatio…
math.AP2021
Mean value properties of solutions to the Helmholtz and modified Helmholtz equations
Nikolay Kuznetsov
Mean value properties of solutions to the -dimensional Helmholtz and modified Helmholtz equations are considered. An elementary derivation of these properties is given; it invol…