M bius inversion formula and inverting lattice sums
Rick P. Millane · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
The M&diaero;bius inversion formula is an interesting theorem from number theory that has application to a number inverse problems, particularly lattice problems. Specific inverse problems, however, often require related M&diaero;bius inversion formulae that can be derived from the fundamental formula. Derivation of such formulae is not easy for the non- specialist, however. Examples of the kinds of inversion formulae that can be derived and their application to inverse lattice problems are described.