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Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
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István Mező
Veröffentlicht/Copyright:
10. März 2010
Abstract
We rephrase Fridli's result [Fridli, Acta Math. Hungar. 45: 393–396, 1985] on the modulus of continuity with respect to a Vilenkin group in the Lebesgue space. We show that this result is valid in the logarithm space and for Vilenkin-like systems. In addition, we prove that there is a strong connection between the best approximation of Fourier series and the modulus of continuity, not only in the Lebesgue space [Gát, Acta Math. Acad. Paedagog. Nyhzi. (N.S.) 17: 161–169, 2001] but in the logarithm space too. We formulate two variable generalizations of the obtained results, which have not been known till now even in the Walsh case.
Key words and phrases:: Modulus of continuity; best approximation; Vilenkin-like systems; logarithm space
Received: 2005-04-04
Revised: 2006-01-24
Published Online: 2010-03-10
Published in Print: 2006-June
© Heldermann Verlag
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Schlagwörter für diesen Artikel
Modulus of continuity;
best approximation;
Vilenkin-like systems;
logarithm space
Artikel in diesem Heft
- Semimartingale Local Time and the American Put Option
- Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions
- A Generalization of Bihari's Lemma for Discontinuous Functions and Its Application to the Stability Problem of Differential Equations with Impulse Disturbance
- Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach
- The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces
- On the Continuity of the Nemytskij Operator between the Spaces 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋)
- Monadic 𝐵𝐿-Algebras
- Rate of Approximation for Certain Durrmeyer Operators
- On Decompositions of a Cube into Cubes and Simplexes
- A Positive Answer to Velichko's Question
- An Inverse Result in Simultaneous Approximation by Modified Beta Operators
- Weyl's Theorem for Algebraically (𝑝, 𝑘)-Quasihyponormal Operators
- Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
- Exact Distributions of the Product and Ratio of Absolute Values of Pearson Type VII and Bessel Function Random Variables
- An Automatically Stable and Order Three Split Rational Approximation of a Semigroup
- Selfadjoint Operators and Generalized Central Algorithms in Frechet Spaces
- Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
- Corrections to “On a Singular Direction of a Meromorphic Function”