Дослідження комплекснозначних власних функцій для струнного хреста

The spectral problem on a string cross with the terms of the boundary conditions of q-periodicity, the contact conditions , balance condition of tension in the overall site is considered. The calculation results gave out the complex-valued eigenfunctions. For two-demensional and three- demensional cross string we have two-demensional and one-demensional eigenspaces. Their structure depend on parameter q.