On the Basicity of Systems of Sines and Cosines with a Linear Phase in Morrey-Type Spaces

In this work systems of sines \sin \left(n+\beta \right)t,\, \, n=۱,۲, \ldots, and cosines \cos \left(n-\beta \right)t,\, \, n=۰,۱,۲, \ldots, are considered, where \beta \in R-is a real parameter. The subspace M^{p,\alpha } \left(۰,\pi \right) of the Morrey space L^{p,\alpha } \left(۰,\pi \right) in which continuous functions are dense is considered. Criterion   for the completeness, minimality and basicity of these systems with respect to the parameter \beta   in the subspace  M^{p,\alpha } \left(۰,\pi \right), ۱