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Completeness of the trigonometric system for the classes \(\varphi (L)\). (English. Russian original) Zbl 1136.46026

Math. Notes 81, No. 5, 632-637 (2007); translation from Mat. Zametki 81, No. 5, 707-712 (2007).
Summary: We obtain a necessary and sufficient condition for the completeness of the trigonometric system with gaps for the classes \(\varphi (L)\).

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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