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.