TY - JOUR
T1 - On the Hilbert operator and the Hilbert formulas on the unit sphere for the time-harmonic Maxwell equations
AU - Pérez-De La Rosa, M. A.
AU - Shapiro, M.
N1 - Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - In this work we establish some analogues of the Hilbert formulas on the unit sphere for the theory of time-harmonic (monochromatic) electromagnetic fields. Our formulas relate one of the components of the limit value of a time-harmonic electromagnetic field in the unit ball to the rest of components. The obtained results are based on the close relation between time-harmonic solutions of the Maxwell equations and the three-dimensional α-hyperholomorphic function theory. Hilbert formulas for α-hyperholomorphic function theory for α being a complex number are also obtained, such formulas relate a pair of components of the boundary value of an α-hyperholomorphic function in the unit ball to the other pair of components, in an analogy with what happens in the case of the theory of functions of one complex variable.
AB - In this work we establish some analogues of the Hilbert formulas on the unit sphere for the theory of time-harmonic (monochromatic) electromagnetic fields. Our formulas relate one of the components of the limit value of a time-harmonic electromagnetic field in the unit ball to the rest of components. The obtained results are based on the close relation between time-harmonic solutions of the Maxwell equations and the three-dimensional α-hyperholomorphic function theory. Hilbert formulas for α-hyperholomorphic function theory for α being a complex number are also obtained, such formulas relate a pair of components of the boundary value of an α-hyperholomorphic function in the unit ball to the other pair of components, in an analogy with what happens in the case of the theory of functions of one complex variable.
KW - Electromagnetic theory
KW - Hilbert operator
KW - Hyperholomorphic functions
KW - Maxwell equations
KW - Singular integrals
UR - http://www.scopus.com/inward/record.url?scp=84908281318&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2014.09.108
DO - 10.1016/j.amc.2014.09.108
M3 - Artículo
SN - 0096-3003
VL - 248
SP - 480
EP - 493
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -