On Basis Properties of Function Systems in Lebesgue Spaces

Some approximative issues related to function systems in Lebesgue spaces are treated in this work, such as the continuation of basis, the non-minimality of basis in subinterval, the relationship between completeness and minimality 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 summands in expressions of these systems.