Construction of solutions of a partial differential equation with constant coefficients using the form of formal series. II (Q1901190)

The paper is the second part of the authors' paper published in Lith. Math. J. 31, No. 3, 285-292 (1991); translation from Litov. Mat. Sb. 31, No. 3, 411-419 (1991; Zbl 0786.35024). Using polynomial solutions of regular differential equations from the first part of the paper and commutative composition of the operator \[ Lu(x, y)= \sum_{nk+ ml= d} a_{kl} D_x^k D_y^l u(x, y), \] where \(a_{kl}\) are complex constants, the authors present the set of independent polynomial solutions of the equation \(Lu= 0\).