Integral representations of generalized axially symmetric potentials in a simply connected domain
AbstractWe obtain integral representations of generalized axially symmetric potentials via analytic functions of a complex variable that are defined in an arbitrary simply connected bounded domain symmetric with respect to the real axis. We prove that these integral representations establish a one-to-one correspondence between analytic functions of a complex variable that take real values on the real axis and generalized axially symmetric potentials of certain classes.
How to Cite
Gryshchuk, S. V., and S. A. Plaksa. “Integral Representations of Generalized Axially Symmetric Potentials in a Simply Connected Domain”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 2, Feb. 2009, pp. 160-77, https://umj.imath.kiev.ua/index.php/umj/article/view/3012.