Generalized Spaces of Type S and Evolutionary Pseudodifferential Equations

We study the main operations (argument shift, differentiation, etc.) in generalized spaces of type S and some classes analytic functions pseudodifferential operators this kind, as well properties Fourier transforms functions, convolutions, convolvers, multiplicators. The correct solvability nonlocal time problem is proved for one class equations S. Its solution presented form convolution fundamental with an initial function, which element space ultradistribution type.