On uniqueness for series in the general Franklin system

DOI10.4213/SM9933EzbMATH Open1544.42014MaRDI QIDQ6582280

Gegham Gevorkian

Publication date: 2 August 2024

Published in: Sbornik: Mathematics (Search for Journal in Brave)

zbMATH Keywords

uniqueness theoremFranklin systemFourier-Franklin seriesgeneral Franklin systemFranklin series

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization (42A63)

Cites Work

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• Uniqueness theorems for series in the Franklin system
• Differentiation of integrals in \(\mathbb{R}^n\)
• Projections onto piecewise linear functions
• A set of continuous orthogonal functions.
• \(\lambda\)-convergence of multiple Walsh-Paley series and sets of uniqueness
• Uniqueness theorems for series by Vilenkin system
• Sum of everywhere convergent trigonometric series
• Uniqueness theorems for generalized Haar systems
• On a ``Martingale property of Franklin series
• Comparison of two generalized trigonometric integrals
• Decomposition of dyadic measures and unions of closed \( \mathcal{U}\)-sets for series in a Haar system
• On a problem of Gevorkyan for the Franklin system
• On the uniqueness of series in the Franklin system
• Uniqueness theorems for simple trigonometric series with application to multiple series
• Uniqueness theorems for Franklin series converging to integrable functions
• Unconditionality of general Franklin systems in L^p[0,1], 1<p<∞
• Uniqueness of series in the Franklin system and the Gevorkyan problems
• Cantor uniqueness and multiplicity along subsequences
• Uniqueness of series by general Franklin system with convergent subsequence of partial sums
• On uniqueness for Franklin series with a convergent subsequence of partial sums

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