TY - JOUR
AU - S. V. Gryshchuk
PY - 2022/01/24
Y2 - 2022/08/16
TI - Monogenic functions with values in commutative complex algebras of the second rank with unity and the generalized biharmonic equation with double characteristics
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 74
IS - 1
SE - Research articles
DO - 10.37863/umzh.v74i1.6948
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/6948
AB - UDC 517.9We prove that any two-dimensional algebra $\mathbb{B}_{\ast}$ of the second rank with unity over the field of complex numbers $\mathbb{C}$ contains basises $\{e_1,e_2\},$ for which the $\mathbb{B}_{\ast}$-valued ``analytic'' functions $\Phi(xe_1+ye_2),$ where $x$ and $y$ are real variables, satisfy a homogeneous PDE of the fourth order with complex coefficients such that its characteristic equation has just one multiple root and the other roots are simple.The set of all triples $(\mathbb{B}_{\ast}, \{e_1,e_2\}, \Phi)$ is described in the explicit form.
ER -