Orthogonal bases for LP spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1971 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 10, pages 648-654 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Gerasimov, S. F.;

doi: 10.1007/bf01106459

Orthogonal bases for LP spaces

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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.

Related Organizations

Saratov State University
Russian Federation

Keywords

Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

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