Basicity of the systems of sines and cosines with linear phases in grand-Sobolev spaces

Abstract

In this work systems of sines 1∪ {sin (n − β)t}n≥1 and 1∪ {cos (n − β)t}n≥1 cosines are considered, where β is real parameter. Criterion for the completeness, minimality and basicity of these systems with respect to the parameter β in one subspace of grand-Sobolev space are found.