On some extremal problems of approximation theory of functions on the real axis I

On the best mean square approximations by entire functions of exponential type in L 2(ℝ) and mean ν-widths of some functional classes

“…A review of the obtained results in this direction can be found, for example, in [1], where one adduces a sufficiently complete comparative chronology of exact solutions to extremal problems of the indicated type, which are obtained on the classes of 2π-periodic functions in the space L 2 ([0, 2π]) and on the classes of functions defined on R and belonging to the space L 2 (R).…”

“…The unimprovability of inequality (1) means that in the space L 2 ([0, 2π]) there exists a function which transforms (1) into the equality…”