Abstract
The spectrum of a system of functions which are orthogonal on [0, 1] is the set of all p ∈ [1, ∞] such that the system forms a basis in Lp[0, 1] (L∞=C). A set E is called aspectral set if there exists a system of functions orthonormal on [0, 1] whose spectrum is E. In this note we determine all spectral sets and construct an orthonormal system corresponding to each of them.
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