The spaces of exponential type vectors of complex degrees of positive operators
New classes of interpolation spaces of exponential type vectors of complex degrees of positive operators are defined. Properties of the approximation spaces generated by the considered interpolation spaces are investigated. An example of application of constructed theory to the regular elliptic boundary problems is considered. In the example exponential type vectors coincide with root vectors. On the other hand, for operators with constant coefficients the set of exponential type vectors is subclass of whole functions of exponential type.