So me appro ximative issues related to function systems in Lebesgue spaces are treated in this work, such as the continuation of basis, the non-min imality of basis in subinterval, the relationship between completeness and min imality of sine and cosine type systems. It is proved that the basis properties of sines and cosines type systems in Lebesgue space of functions depend on the number of exponential su mmands in expressions of these systems.
This paper is devoted to the study of basis properties of the system {t} ∪ e i(n+β sign n)t n∈Z , where β is a real parameter, in Morrey-Sobolev-type spaces. We find sufficient conditions for the basicity in Morrey-Sobolev-type spaces in terms of inequalities of the parameter β .
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