The perturbed system of exponents with a piecewise linear phase, consisting of eigenfunctions of a discontinuous differential operator, is considered in this work. Under certain conditions on the weight function of the form of a power function, sufficient conditions for the basicity of this system are obtained in generalized weighted Lebesgue space.
Generalized concepts of b-completeness, b-independence, b-minimality, and b-basicity are introduced. Corresponding concept of a space of coefficients is defined, and some of its properties are stated.
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