In this paper, we consider the restoration problem for solutions of the generalized Cauchy- Riemann system in a multidimensional spatial domain using their values on a piece of the boundary of the domain, i. e., the Cauchy problem. We construct an approximate solution of this problem based on the Carleman matrix method.
Abstract
Using Carleman linearization an approximation is given for the solution of a system at Hopf bifurcation. The values of the Poincaré-Lyapunov constants (whether they are zero or not) affect the linear algebraic properties of the Carleman matrix and they appear in solvability conditions (through the Fredholm alternative). We provide a linear algebra based algorithm to compute the Poincaré-Lyapunov constants.
Carleman’s Formula for Solutions of the Generalized Cauchy-Riemann System in Multidimensional Spatial Domain