|ISSN 1088-6850(online) ISSN 0002-9947(print)|
Restricted mean values and harmonic functions
Abstract: A function h defined on a region R in will be said to possess a restricted mean value property if the value of the function at each point is equal to the mean value of the function over one open ball in R, with centre at that point. It is proved here that this restricted mean value property implies h is harmonic under certain conditions.
Retrieve articles in Transactions of the American Mathematical Society with MSC: 31B05
Retrieve articles in all journals with MSC: 31B05