Mellin transforms on binary fields (Q1577561)

Some boundedness and inversion results are proved for a large class of operators on binary fields, i.e., on 2-series and 2-adic fields. As a special case, it is obtained, that the Mellin transform on any binary field can be extended to a bounded linear isometry on \(L_2\). An explicit formula for the inverse Mellin transform is given and it is shown that the inversion holds when the Mellin transform is integrable.