Some ramifications of a theorem of Boas and Pollard concerning the completion of a set of functions in 𝐿²

DOI10.1090/S0002-9947-97-02034-5zbMath0892.46008OpenAlexW1576903265MaRDI QIDQ4372603

Robert E. Zink, Kazaros Kazarian

Publication date: 16 December 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-02034-5

zbMATH Keywords

Schauder basisapproximate continuitybounded measurable function\(M\)-basismultiplicative completionweighted \(L^p\)-spacesquasibasis

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Approximation by other special function classes (41A30)

Related Items (7)

Subsystems of the Walsh orthogonal system whose multiplicative completions are quasibases for $L^\{p\}[0,1$, $1\leq p < +\infty $] ⋮ Duals of weighted exponential systems ⋮ Biorthonormal systems in Freud-type weighted spaces with infinitely many zeros -- an interpolation problem ⋮ On the multiplicative completion of centered systems. ⋮ Nonnegativity constraints for structured complete systems ⋮ Reflections on a Theorem of Boas and Pollard ⋮ On the existence of universal series by trigonometric system

Cites Work

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• Summability of generalized Fourier series and Dirichlet's problem in \(L^ p(d\mu)\) and weighted \(H^ p\)-spaces \((p>1)\)
• On the multiplicative completion of some incomplete orthonormal systems to bases in \(L^p\), \(1\leq p\infty\)
• On sets of functions that can be multiplicatively completed
• Basic Sequences in the Space of Measurable Functions
• THE REPRESENTATION OF MEASURABLE FUNCTIONS BY SERIES
• On the Multiplicative Completion of Certain Basic Sequences in L p , 1 < p < &#8734
• The multiplicative completion of sets of functions

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