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Some Negative Results Concerning the Process of Fejér Type Trigonometric Convolution
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G. Oniani
Published/Copyright:
February 23, 2010
Abstract
The process of Fejér type trigonometric convolution and its discrete analogue have equivalent uniform residues. The situation changes under pointwise comparison. In this direction negative results have been obtained by different authors. One result of such a type is given in the present paper. In particular, a counter-example is constructed for which both comparisons diverge on the set of complete measure. The smoothness of the counter-example as well as some other problems are investigated.
Key words and phrases.: Sequence of convolution operators; sequence of discrete analogues of convolution operators; Fejér type kernels; pointwise comparison
Received: 1994-12-16
Published Online: 2010-02-23
Published in Print: 1995-June
© 1995 Plenum Publishing Corporation
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- On Structure of Solutions of a System of Four Differential Inequalities
- On the Darboux Transformation. I
- Kneser-Type Oscillation Criteria for Self-Adjoint Two-Term Differential Equations
- Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. II
- Weighted Reverse Weak Type Inequality for General Maximal Functions
- On a Generalization of the Keldysh Theorem
- On a Spatial Problem of Darboux Type for a Second-Order Hyperbolic Equation
- Some Negative Results Concerning the Process of Fejér Type Trigonometric Convolution
- Applications of the Method of Barriers II. Some Singularly Perturbed Problems
Keywords for this article
Sequence of convolution operators;
sequence of discrete analogues of convolution operators;
Fejér type kernels;
pointwise comparison
Articles in the same Issue
- On Structure of Solutions of a System of Four Differential Inequalities
- On the Darboux Transformation. I
- Kneser-Type Oscillation Criteria for Self-Adjoint Two-Term Differential Equations
- Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. II
- Weighted Reverse Weak Type Inequality for General Maximal Functions
- On a Generalization of the Keldysh Theorem
- On a Spatial Problem of Darboux Type for a Second-Order Hyperbolic Equation
- Some Negative Results Concerning the Process of Fejér Type Trigonometric Convolution
- Applications of the Method of Barriers II. Some Singularly Perturbed Problems
