On the Hilbert's Technique for Use in Diffraction Prob- lems Described in Terms of Bicomplex Mathematics

摘要

It is shown from the Hilbert's theory that if the real function Ⅱ(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factorπ~+(θ) and its complex conjugate π~-(θ)(=π~+(θ)). This factorization is tested to decompose a real far-zone field pattern having zeros. To this end, the factorized factors are described in terms of bicomplex mathematics. In our bicomplex mathematics, the temporal imag- inary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i~2=-1 and j~2=-1.