On the construction of solutions to a class of multidimensional generalized Cauchy-Riemann systems with singular coefficients

The article is devoted to the study of one class of multidimensional generalized Cauchy-Riemann systems with singular coefficients of the form -𝛼 -𝛽𝐴, here 𝛼,-| |𝛽 - real numbers such that + > 0 and 𝛽 - an integer, - a complex matrix of the order . By moving to the polar coordinates, the solutions of the system are searched for in the form of a trigonometric series of = 𝑔 with unknown coefficients ( ), depending on from = . For these unknown coefficients, the related Bessel equa-tions are obtained, in which the coefficient for the desired vector function has the form: (2𝛼 + ) + 4 2(1-𝛼-𝛽)𝐴𝐴, a unit matrix of the order of . Depending on 𝛼, 𝛽and the eigenvalues of of the matrix 𝐴𝐴, general solutions of the last equations are found,then the general solution of the original system is written out. It should be noted that in the case when the matrix has eigenvalues that are not semisimple, i.e. having unequal algebraic and geometric multiplicities, it is necessary to solve inhomogeneous related Bessel equations by the method of variation of arbitrary constants. From the found general solution of the system, it is possible to distinguish regular, i.e. having no singularities in the finite part of the plane, as well as solutions to boundary value problems.