The existence of a weighted mean for almost periodic functions (Q544191)

There is a question of the existence of a weighted mean for almost periodic functions. It is known that there exist weights for which a weighted mean for almost periodic functions may or may not exist. In the paper under review sufficient conditions are given which guarantee the existence of a weighted mean for almost periodic functions, which then will coincide with the classical Bohr mean. Moreover, it is shown that under these conditions, the corresponding weighted Bohr transformation exists.