BASES IN COMMUTATIVE ALGEBRAS OF SECOND RANK AND MONOGENIC FUNCTIONS RELATED TO GENERALIZED BIHARMONIC EQUATION WITH SIMPLE CHARACTERISTICS
DOI:
https://doi.org/10.15407/dopovidi2025.06.003Keywords:
generalized biharmonic equation, commutative and associative algebra, monogenic functionAbstract
All commutative and associative algebras and their bases, such that hypercomplex monogenic functions defined on linear manifolds generated by these bases and having images in the corresponding algebra of the second rank, have component functions satisfying the generalized biharmonic equation with simple characteristics including zero, are found. Moreover, descriptions are found for all triples consisting of two-dimensional commutative algebras over the field of complex numbers, their bases, and monogenic functions with values in these algebras, such that the components of the monogenic functions satisfy this generalized biharmonic equation. An algorithm for constructing solutions of this generalized biharmonic equation using the components of various monogenic functions has been found.
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