Uniform convergence with rates of general singular operators
-
George A. Anastassiou
ganastss@memphis.edu
-
Razvan A. Mezei
rmezei@memphis.edu
Downloads
DOI:
https://doi.org/10.4067/s0719-06462013000200001Abstract
In this article we study the approximation properties of general singular integral operators over the real line. We establish their convergence to the unit operator with rates. The estimates are mostly sharp and they are pointwise or uniform. The established inequalities involve the higher order modulus of smoothness. We apply this theory to the trigonometric singular operators.
Keywords
Most read articles by the same author(s)
- George A. Anastassiou, Right general fractional monotone approximation , CUBO, A Mathematical Journal: Vol. 17 No. 3 (2015): CUBO, A Mathematical Journal
- George A. Anastassiou, Quantitative Approximation by a Kantorovich-Shilkret quasi-interpolation neural network operator , CUBO, A Mathematical Journal: Vol. 20 No. 3 (2018)
- George A. Anastassiou, Approximation by discrete singular operators , CUBO, A Mathematical Journal: Vol. 15 No. 1 (2013): CUBO, A Mathematical Journal
- George A. Anastassiou, Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators , CUBO, A Mathematical Journal: Vol. 20 No. 1 (2018)
- George A. Anastassiou, Foundations of generalized Prabhakar-Hilfer fractional calculus with applications , CUBO, A Mathematical Journal: Vol. 23 No. 3 (2021)
- George A. Anastassiou, Higher order multivariate Fuzzy approximation by basic neural network operators , CUBO, A Mathematical Journal: Vol. 16 No. 3 (2014): CUBO, A Mathematical Journal
- George A. Anastassiou, Multiple general sigmoids based Banach space valued neural network multivariate approximation , CUBO, A Mathematical Journal: Vol. 25 No. 3 (2023)
- George A. Anastassiou, Fractional Voronovskaya type asymptotic expansions for quasi-interpolation neural network operators , CUBO, A Mathematical Journal: Vol. 14 No. 3 (2012): CUBO, A Mathematical Journal
- Razvan A. Mezei, Applications and Lipschitz results of approximation by smooth Picard and Gauss-Weierstrass type singular integrals , CUBO, A Mathematical Journal: Vol. 13 No. 3 (2011): CUBO, A Mathematical Journal
- George A. Anastassiou, Poincar´e Type Inequalities for Linear Differential Operators , CUBO, A Mathematical Journal: Vol. 10 No. 3 (2008): CUBO, A Mathematical Journal
Similar Articles
- Carlos Cesar Aranda, Spacetime singularity, singular bounds and compactness for solutions of the Poisson‘s equation , CUBO, A Mathematical Journal: Vol. 17 No. 2 (2015): CUBO, A Mathematical Journal
- D. Goeleven, An Expository Discussion on Singular Inequality Problems and Equilibrium Models in Economics , CUBO, A Mathematical Journal: Vol. 6 No. 1 (2004): CUBO, A Mathematical Journal
- George A. Anastassiou, Converse Fractional Opial Inequalities for Several Functions , CUBO, A Mathematical Journal: Vol. 10 No. 1 (2008): CUBO, A Mathematical Journal
- Roberto Dieci, Gian-Italo Bishi, Laura Gardini, Routes to Complexity in a Macroeconomic Model Described by a Noninvertible Triangular Map , CUBO, A Mathematical Journal: Vol. 5 No. 3 (2003): CUBO, Matemática Educacional
- Luiz Antonio Pereira Gomes, Eduardo Brandani da Silva, A Characterization of the Product Hardy Space 𻹠, CUBO, A Mathematical Journal: Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal
- Iris A. López, On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup , CUBO, A Mathematical Journal: Vol. 19 No. 2 (2017): CUBO, A Mathematical Journal
- Stephen McDowall, Optical Tomography for Media with Variable Index of Refraction , CUBO, A Mathematical Journal: Vol. 11 No. 5 (2009): CUBO, A Mathematical Journal
- Edoardo Ballico, Osculating varieties and their joins: \(\mathbb{P}^1\times \mathbb{P}^1\) , CUBO, A Mathematical Journal: Vol. 25 No. 2 (2023)
- Mahdi Zreik, On the approximation of the δ-shell interaction for the 3-D Dirac operator , CUBO, A Mathematical Journal: Vol. 26 No. 3 (2024)
- Colette Anné, Anne-Marie Charbonnel, Bohr-Sommerfeld conditions for several commuting Hamiltonians , CUBO, A Mathematical Journal: Vol. 6 No. 2 (2004): CUBO, A Mathematical Journal
<< < 1 2 3 4 5 6 7 8 9 10 11 12 > >>
You may also start an advanced similarity search for this article.
Downloads
Download data is not yet available.
Published
2013-06-01
How to Cite
[1]
G. A. Anastassiou and R. A. Mezei, “Uniform convergence with rates of general singular operators”, CUBO, vol. 15, no. 2, pp. 01–19, Jun. 2013.
Issue
Section
Articles
