Engineering topics
Publications and source records attributed to Lebedev, Vladimir V.
We consider the class PW(R{sup n}) of functions in L{sup 2}(R{sup n}), whose Fourier transform has bounded support. We obtain a description of continuous maps {phi}:R{sup m}{yields}R{sup n} such that fo{phi} element of PW(R{sup m}) for every function f element of PW(R{sup n}). Only injective affine maps {phi} have this property. Bibliography: 5 titles.
We consider the spaces A{sub p}(T) of functions f on the circle T such that the sequence of Fourier coefficients f-hat={l_brace}f-hat(k), k element of Z{r_brace} belongs to l{sup p}, 1{<=}p<2. The norm in A{sub p}(T) is defined by ||f||{sub A{sub p}}=||f-hat||{sub l}{sup P}. We study the rate of growth of the norms ||e{sup i{lambda}{phi}|}|{sub A{sub p}} as |{lambda}|{yields}{infinity}, {lambda} element of R, for C{sup 1}-smooth real functions {phi} on T. The results have natural applications to the problem of changes of variable in the spaces A{sub p}(T). Bibliography: 17 titles.