Abstract
AbstractIn this paper we study an analogue of the Cauchy‐type integral for the theory of time‐harmonic solutions of the relativistic Dirac equation in case of a piece‐wise Liapunov surface of integration and we prove the Sokhotski–Plemelj theorem for it as well as the necessary and sufficient condition for the possibility to extend a given Hölder function from such a surface up to a solution of the relativistic Dirac equation in a domain. Formula for the square of the singular Cauchy‐type integral is given. The proofs of all these facts are based on intimate relations between time‐harmonic solutions of the relativistic Dirac equation and some versions of quaternionic analysis. Copyright © 2002 John Wiley & Sons, Ltd.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
