5 papers
A characterisation of harmonic functions by quadrature identities of annular domains and related results
Nikolay Kuznetsov
A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within t…
Weighted means of harmonic functions and characterization of balls
Nikolay Kuznetsov
Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions.…
Inverse mean value properties (a survey)
Nikolay Kuznetsov
Several mean value identities for harmonic and panharmonic functions are reviewed along with the corresponding inverse properties. The latter characterize balls, annuli and strips…
Asymptotic mean value properties of meta- and panharmonic functions
Nikolay Kuznetsov
Asymptotic mean value properties, their converse and some other related results are considered for solutions to the -dimensional Helmholtz equation (metaharmonic functions) and…
Mean value properties of harmonic functions and related topics (a survey)
Nikolay Kuznetsov
Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be…