Carleman's Formulas in Complex Analysis: Theory and Applications

Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com­ plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a domain D a holomorphic function that is sufficiently well-behaved when approaching the bound...