TY - JOUR
T1 - On the Hilbert formulas on the unit sphere for the time-harmonic relativistic Dirac bispinors theory
AU - Pérez-de la Rosa, Marco Antonio
N1 - Funding Information:
The author was partially supported by CONACYT and by Instituto Politécnico Nacional as Doctoral scholarship and PIFI scholarship recipient.
PY - 2014/8/15
Y1 - 2014/8/15
N2 - In this paper there are established some analogues of the Hilbert formulas on the unit sphere for the theory of time-harmonic (monochromatic) relativistic Dirac bispinors. The formulas relate a pair of the components of the limit value of a time-harmonic Dirac bispinor in the unit ball to the other pair of components. The obtained results are based on the intimate connection between time-harmonic solutions of the relativistic Dirac equation and the three-dimensional α-hyperholomorphic function theory. Hilbert formulas for α-hyperholomorphic function theory for α being a complex quaternionic number are also presented, 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 is known for the case of the theory of functions of one complex variable.
AB - In this paper there are established some analogues of the Hilbert formulas on the unit sphere for the theory of time-harmonic (monochromatic) relativistic Dirac bispinors. The formulas relate a pair of the components of the limit value of a time-harmonic Dirac bispinor in the unit ball to the other pair of components. The obtained results are based on the intimate connection between time-harmonic solutions of the relativistic Dirac equation and the three-dimensional α-hyperholomorphic function theory. Hilbert formulas for α-hyperholomorphic function theory for α being a complex quaternionic number are also presented, 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 is known for the case of the theory of functions of one complex variable.
KW - Hilbert operator
KW - Hyperholomorphic functions
KW - Relativistic Dirac bispinors theory
KW - Singular integrals
UR - http://www.scopus.com/inward/record.url?scp=84895775147&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2014.02.034
DO - 10.1016/j.jmaa.2014.02.034
M3 - Artículo
SN - 0022-247X
VL - 416
SP - 575
EP - 596
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -