Carleman’s formula for the generalized Cauchy-Riemann system : Carleman’s formula for the generalized Cauchy-Riemann system - Ermamatova, Fotima E.; Ermamatova, Bibixojar E. (MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS, 2024)
Using results from [2], [3], [4] on solving the Cauchy problem, we construct the Carleman matrix for the Laplace and Helmholts equations in explicit form and, on its basis, the regularized solution of the Cauchy problem for system (1). By using the continuation formula we found necessary and sufficient for the extendibility of functions given an a part of a boundary to the domain as a solution of the system (1). We prove the Fock-Kyni theorem fore this one.