on the basicity of systems of sines and cosines with a linear phase in morrey-type spaces

In this work systems of sines sin (n + β)t, n = 1, 2, . . . , and cosines cos (n − β)t, n = 0, 1, 2, . . . , are considered, where β ∈ r−is a real parameter. the subspace mp,α (0, π) of the morrey space l p,α (0, π) in which continuous functions are dense is considered. criterion for the completeness, minimality and basicity of these systems with respect to the parameter β in the subspace mp,α (0, π), 1 < p < +∞, are found.