BASICITY OF A PERTURBED SYSTEM OF EXPONENTS IN LEBESGUE SPACES WITH A VARIABLE SUMMABILITY EXPONENT

In this paper a system of exponents 1 is considered, where is some polynomial of degree m, m ∈ N. It is proved that under certain conditions on the exponent p (·) the basicity of this system in a Lebesgue space with a variable summability exponent Lp(·) (−π, π) depends on the coefficient αm−1 and m. Moreover, in the case of basicity, it is isomorphic to the classical system of exponents in Lp(·) (−π, π). Earlier in the case the Riesz basicity of this system in L2 (−π, π) was established by Yu.A.Kazmin

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