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On the Uniform Convergence and 𝐿-Convergence of Double Fourier Series with Respect to the Walsh–Kaczmarz System
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U. Goginava
Published/Copyright:
March 3, 2010
Abstract
In this paper we study the approximation by rectangular partial sums of a double Fourier series with respect to the Walsh–Kaczmarz system in the spaces 𝐶 and 𝐿. From our results we obtain different criteria of the uniform convergence and 𝐿-convergence of a double Fourier–Kaczmarz series.
Key words and phrases:: Walsh–Kaczmarz system; convergence in 𝐿-norm; bounded variation in the sense of Hardy; uniform convergence
Received: 2002-04-28
Published Online: 2010-03-03
Published in Print: 2003-June
© Heldermann Verlag
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Articles in the same Issue
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- On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups
- On the Uniform Convergence and 𝐿-Convergence of Double Fourier Series with Respect to the Walsh–Kaczmarz System
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Keywords for this article
Walsh–Kaczmarz system;
convergence in 𝐿-norm;
bounded variation in the sense of Hardy;
uniform convergence
Articles in the same Issue
- On ARU-Resolutions of Uniform Spaces
- On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups
- On the Uniform Convergence and 𝐿-Convergence of Double Fourier Series with Respect to the Walsh–Kaczmarz System
- Dynamic Programming and Mean-Variance Hedging in Discrete Time
- Extending Quasi-Invariant Measures by Using Subgroups of a Given Group
- Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems
- General 𝑀-Estimators in the Presence of Nuisance Parameters. Skew Projection Technique
- A Unified Characterization of 𝑞-Optimal and Minimal Entropy Martingale Measures by Semimartingale Backward Equations
- On the Existence of Continuous Modifications of Vector-Valued Random Fields
- Weak Convergence of a Dirichlet-Multinomial Process
- Time-Dependent Barrier Options and Boundary Crossing Probabilities
- On Separation Properties for Families of Probability Measures
- Oscillation Theorems of Nonlinear Difference Equations of Second Order
- On Bounds for the Characteristic Functions of Some Degenerate Multidimensional Distributions
- Estimates of Fourier Coefficients
- On Approximate Large Deviations for 1D Diffusion