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On the Convergence of Conjugate Trigonometric Polynomials
Published/Copyright:
March 10, 2010
Abstract
Sufficient conditions are found, under which for 𝑓 ∈ 𝐶([–π, π]) or 𝑓 ∈ 𝐿([–π, π]) the convergence of a sequence of trigonometric polynomials in the norms of these spaces implies the convergence of their conjugates in the same norms.
Received: 2006-02-10
Revised: 2006-05-15
Published Online: 2010-03-10
Published in Print: 2006-September
© Heldermann Verlag
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Keywords for this article
Conjugate functions;
de la Vallée-Poussin means;
best approximation
Articles in the same Issue
- Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term
- Curves with Two Pencils and Associated Maps to Projective Spaces
- The Second Obstruction Functor
- Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
- Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series
- On the Convergence of Conjugate Trigonometric Polynomials
- Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems
- New Proof of the 𝑇(1) Theorem for Triebel–Lizorkin Spaces
- Inversion of Ahlfors and Grunsky Inequalities
- On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces
- Computing Characteristic Sets of Ordinary Radical Differential Ideals
- Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
- On Systems of Linear Functional Differential Inequalities
- The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight
- Fourier Series with Small Gaps
- Oscillations of Higher Order Functional Differential Equations with Impulses