Necessary and Sufficient Conditions for Associated Pairs in Quaternionic Analysis

  • Le Hung Son
  • Nguyen Van Thanh
Conference paper
Part of the Trends in Mathematics book series (TM)


This paper deals with the initial value problem of the type
$$ \frac{{\partial w}} {{\partial t}} = L\left( {t,x,w,\frac{{\partial w}} {{\partial x_i }}} \right) $$
$$ w(0,x) = \phi (x) $$
where t is the time, L is a linear differential operator of first order in Quaternionic Analysis and ϕ is a regular function taking values in the Quaternionic Algebra. The necessary and sufficient conditions on the coefficients of the operator L under which L is associated to the generalized Cauchy-Riemann operator of the Quaternionic Analysis are proved.

This criterion makes it possible to construct the operator L for which the initial problem (1),(2) is solvable for an arbitrary initial regular function ϕ and the solution is also regular for each t.


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Le Hung Son
    • 1
  • Nguyen Van Thanh
    • 2
  1. 1.Hanoi University of TechnologyHanoiVietnam
  2. 2.Hanoi University of ScienceHanoiVietnam

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