Completeness of the trigonometric system for the classes \(\varphi (L)\)

DOI10.1134/S0001434607050082zbMath1136.46026OpenAlexW1966208037MaRDI QIDQ2473750

Yurii S. Kolomoitsev

Publication date: 4 March 2008

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434607050082

zbMATH Keywords

Jensen's inequalitytrigonometric polynomialParseval's equalityRiesz-Fischer theorem\(2\pi\)-periodic functiontrigonometric system with gaps

Mathematics Subject Classification ID

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

Cites Work

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• Linear continuous functionals and representation of functions by series in the spaces \(E_{\varphi}\)
• Subspaces of \(L^p(G)\) spanned by characters: \(0<p<1\)
• The failure of spectral analysis in 𝐿^{𝑝} for 0<𝑝<1
• Представление функций классовL p [0, 1, 0<p<1, ортогональными рядами]

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