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

Abstract

In this work systems of sines $sin left(n+beta right)t,, , n=1,2, ldots,$ and cosines $cos left(n-beta right)t,, , n=0,1,2, ldots,$ are considered, where $beta in R-$is a real parameter. The subspace $M^{p,alpha } left(0,pi right)$ of the Morrey space $L^{p,alpha } left(0,pi right)$ 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  $M^{p,alpha } left(0,pi right)$, $1