Stable Random Variables with Complex Index α. the Case |α − 1/2| < 1/2

Complex-valued random variables that satisfy usual stability condition for a complex parameter α such that |α − 1/2| < 1/2, are constructed. The characteristic function of the obtained random variables is found and limit theorems for sums of independent identically distributed random variables are proved. The corresponding Lévy processes and semigroups of operators corresponding to these processes are constructed.