Volkova M. Spectral analysis of unconditional expansions by values of the entire vector-functions of one second order of growth

In the thesis in spaces $L_2(0, sigma)$, in an arbitray separable Hilbert spaces and in their Cartesian product of such spaces we investigate the basis properties of families of values of entire vector-functions, whose order of growth is 1/2. In solution of problems considered in the thesis, the vector-functions $c_w(z,t)$ ($w$- quasicosine) with values in the spaces $L_2(0, sigma), sigma > 0$, which are constructed according to $A_2$-Muckenhoupt weights on semiaxis $R_+$ with the help og the canonical procedure, play role of models. The solutions of main problems in the thesis are based on modification of method of integral estimates of the resolvent norms, the obtained results may be applied for study of spectral structure of finite-dimensional pertubations of Volterra operators and for investigation of spectral problems connected with canonical systems of differential equations.