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Completeness of the system {z(lambda n)} in L-2[B, alpha(0)]

Abstract: Let B be an unbounded domain located outside an angle domain with vertex at the origin, Lambda = {lambda(n)}(n = 1, 2,...) be a sequence of complex numbers satisfying sup | arg(lambda(n) )| < alpha < pi/2 and denote by M(Lambda) = {z(lambda), lambda epsilon Lambda} the corresponding system of functions z(lambda)(lambda epsilon Lambda). Let alpha(0)(z) be a weight function defined on B. We obtain a completeness theorem for the system M(Lambda) in the Hilbert space L-2[B,alpha(0)].