On the Hilbert<cd02147.gif>s Technique for Use in Diffraction Problems Described in Terms of Bicomplex Mathematics

Masahiro HASHIMOTO

On the Hilberts Technique for Use in Diffraction Problems Described in Terms of Bicomplex Mathematics

Masahiro HASHIMOTO

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It is shown from the Hilberts theory that if the real function Π(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factor π⁺(θ) and its complex conjugate 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 imaginary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i²=-1 and j²=-1.

Publication: IEICE TRANSACTIONS on Electronics Vol.E81-C No.2 pp.315-318

Publication Date: 1998/02/25

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Category: Electromagnetic Theory

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Masahiro HASHIMOTO, "On the Hilberts Technique for Use in Diffraction Problems Described in Terms of Bicomplex Mathematics" in IEICE TRANSACTIONS on Electronics, vol. E81-C, no. 2, pp. 315-318, February 1998, doi: .
Abstract: It is shown from the Hilberts theory that if the real function Π(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factor π⁺(θ) and its complex conjugate 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 imaginary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i²=-1 and j²=-1.
URL: https://globals.ieice.org/en_transactions/electronics/10.1587/e81-c_2_315/_p

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@ARTICLE{e81-c_2_315,
author={Masahiro HASHIMOTO, },
journal={IEICE TRANSACTIONS on Electronics},
title={On the Hilberts Technique for Use in Diffraction Problems Described in Terms of Bicomplex Mathematics},
year={1998},
volume={E81-C},
number={2},
pages={315-318},
abstract={It is shown from the Hilberts theory that if the real function Π(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factor π⁺(θ) and its complex conjugate 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 imaginary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i²=-1 and j²=-1.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - On the Hilberts Technique for Use in Diffraction Problems Described in Terms of Bicomplex Mathematics
T2 - IEICE TRANSACTIONS on Electronics
SP - 315
EP - 318
AU - Masahiro HASHIMOTO
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E81-C
IS - 2
JA - IEICE TRANSACTIONS on Electronics
Y1 - February 1998
AB - It is shown from the Hilberts theory that if the real function Π(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factor π⁺(θ) and its complex conjugate 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 imaginary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i²=-1 and j²=-1.
ER -