Abstract
This paper deals with the initial value problem of the type
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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© 2008 Birkhäuser Verlag Basel/Switzerland
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Son, L.H., Van Thanh, N. (2008). Necessary and Sufficient Conditions for Associated Pairs in Quaternionic Analysis. In: Sabadini, I., Shapiro, M., Sommen, F. (eds) Hypercomplex Analysis. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9893-4_13
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DOI: https://doi.org/10.1007/978-3-7643-9893-4_13
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-9892-7
Online ISBN: 978-3-7643-9893-4
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