Complete and incomplete exponential systems in the power weighted spaces on a half-line / A. M. Sedletskii. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 2. P. 52-55 [Moscow Univ. Math. Bulletin. Vol. 69, N 2, 2014.].
We essentially widen the class of sequences λn for which the completeness (non-completeness) of system of exponentials e-λnt, Reλn > 0 is proved in the spaces Lp(R+, tαdt),α > -1. The proof uses the invariance of completeness relative to the change of the weight tα by the weight (1+t)α; this fact is also proved here.
Key words: system of exponentials, completeness, weight space, convolution of functions.