On the asymptotic properties of functions holomorphic in tubular cones

For functions holomorphic in tube domains over a cone, the author studies the connection between their asymptotic behavior at the origin along orbits of one-parameter groups of linear transformations and asymptotic properties of the real parts of the boundary values of these functions. It is shown that, as a rule, the presence of certain asymptotics of the real part of a boundary value of a holomorphic function guarantees similar asymptotics for the whole function within the domain.
Bibliography: 6 titles.