On the solutions of polynomial growth for a multidimensional generalized Cauchy–Riemann system

Abstract

For a multidimensional generalized Cauchy–Riemann system we study the Noether property in Hölder spaces of functions bounded on the whole plane. For the case of constant coefficients we consider the solutions defined on the whole plane or on the half-plane and having a polynomial growth at the infinity. For the two- and three-dimensional cases we find appropriate conditions for the coefficients ensuring that the solutions to the first problem is finite-dimensional or zero or infinite-dimensional, respectively.