Richard G. Cooke

Duplication and Other Formulae for Bessel Functions of Certain Type

IV. There are some remarks that seem relevant. (a) We have stated the theorem for linear sets. It is obvious from the proof that the linearity of the sets is quite inessential and that the proof is valid for sets in Euchdean space of any number of dimensions. If the sets lie in Bn, then we have merely to replace intervals and their lengths in our proof by Convex w-dimensional regions and their diameters respectively. (6) The theorem, proved for closed sets in (0, 1), is obviously true for all bounded closed sets. The University, Manchester.