Funktsiya Karlemana i zadacha Koshi dlya poligarmonicheskikh funktsiy

The book "Karleman Function and Cauchy Problem for Polyharmonic Functions" offers a comprehensive examination of the conditional correctness and the construction of new formulas for the Karleman function, as well as the regularization in the Cauchy problem for polyharmonic functions. It addresses current challenges in the theory of partial differential equations and presents the Karleman function in explicit form. The authors, Zebiniso Ashurova, Nodira Zhuraeva, and Umidakhon Zhuraeva, introduce a family of functions that depend on a parameter and prove that this family converges to a solution of the problem under certain conditions. The book also includes fundamental results and definitions that are essential for understanding polyharmonic functions.