Criteria for Approximative Properties of Systems of Sines and Cosines in Grand Lebesgue Space

In this article the trigonometric systems of sine sin (n - alpha) t, n = 1, 2, ... and cosine cos (n - alpha) t, n = 0, 1, 2, ... are considered in the grand Lebesgue space L-p)(0, pi), where alpha is a real parameter. The basis properties: criteria for minimality, completeness and basicity of these trigonometric systems with respect to the parameter alpha, are found.