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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Translated from Matematicheskie Zametki, Vol. 10, No. 4, pp. 375–385, October, 1971.
This work was completed under the guidance of V. F. Emel'yanov, to whom the author extends warm thanks.
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Gerasimov, S.F. Orthogonal bases for LP spaces. Mathematical Notes of the Academy of Sciences of the USSR 10, 648–654 (1971). https://doi.org/10.1007/BF01106459
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DOI: https://doi.org/10.1007/BF01106459