Spectral analysis of biorthogonal expansions generated by Muckenhoupt weights

An arbitrary Muckenhoupt A₂-weight w² on the special contour ( 1/2) generates a function Y_,w (, t), which for =1, w²(z) 1 coincides with the exponential exp{it}. In the paper, with the aid of B. S. Pavlov's geometric approach, one obtains criteria for the unconditional basis property of families of functions of the form {y,w(_k,t):_k} in the space L₂(0, ). The analytic foundation of the constructions is a generalization of M. M. Dzhrbashyan's certain results (power weight) to the case of arbitrary Muckenhoupt A₂- weights.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 190, pp. 34–80, 1991.