Multidimensional Tauberian theorem for holomorphic functions of bounded argument

For generalized functions whose Laplace transform has a non-negative imaginary part in a tubular region over a positive coordinate angle, sufficient conditions for the existence of a quasi-asymptotics are given, and the regularly varying function with respect to which this quasi-asymptotics exists is found. The results obtained are used to study the asymptotic behavior of solutions to the Cauchy problem for passive operators.