THE UNIFORM, OVER THE WHOLE-LINE-R ESTIMATES OF SPECTRAL EXPANSIONS RELATED TO THE SELF-ADJOINT EXTENSIONS OF THE HILL OPERATOR AND OF THE SCHRODINGER OPERATOR WITH A BOUNDED AND MEASURABLE POTENTIAL

We consider some properties of the spectral expansions related to self adjoint extensions of the operator Hu = -u'' + q(x)u, over the whole l ine R in the case when q(x) is a continuous periodic function (the Hil l operator) and in the case when q(x) is a bounded measurable function . This paper gives a brief description of results obtained in the foll owing directions: the uniform over R estimates of the generalized eige nfunctions, the uniform over R estimates of the spectral function, the uniform over R equiconvergence with the Fourier integral expansion, a nd the uniform over R rate of convergence for functions from the Sobol ev-Liouville classes.