### Abstract

Original language | American English |
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Pages (from-to) | 575-596 |

Number of pages | 22 |

Journal | Journal of Mathematical Analysis and Applications |

DOIs | |

State | Published - 15 Aug 2014 |

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**On the Hilbert formulas on the unit sphere for the time-harmonic relativistic Dirac bispinors theory.** / Pérez-de la Rosa, Marco Antonio.

Research output: Contribution to journal › Article

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

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. © 2014 Elsevier Inc.

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. © 2014 Elsevier Inc.

U2 - 10.1016/j.jmaa.2014.02.034

DO - 10.1016/j.jmaa.2014.02.034

M3 - Article

SP - 575

EP - 596

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

ER -