On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions

<p/> <p>This note is concerned with a comparison of the approximation-theoretical behaviour of trigonometric convolution processes and their discrete analogues. To be more specific, for continuous functions it is a well-known fact that under suitable conditions the relevant uniform error...

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Bibliographic Details
Main Authors:	Nessel RJ, Röpsch C
Format:	Article
Language:	English
Published:	SpringerOpen 1998-01-01
Series:	Journal of Inequalities and Applications
Subjects:	Trigonometric convolution operators Discrete analogues Comparison Stability inequalities
Online Access:	http://www.journalofinequalitiesandapplications.com/content/2/843820

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spelling	doaj-a413a96d71a042b09b7e4aad138c89622020-11-24T21:15:34ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1998-01-0119984843820On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functionsNessel RJRöpsch C<p/> <p>This note is concerned with a comparison of the approximation-theoretical behaviour of trigonometric convolution processes and their discrete analogues. To be more specific, for continuous functions it is a well-known fact that under suitable conditions the relevant uniform errors are indeed equivalent, apart from constants. It is the purpose of this note to extend the matter to the frame of Riemann integrable functions. To establish the comparison for the corresponding Riemann errors, essential use is made of appropriate stability inequalities.</p>http://www.journalofinequalitiesandapplications.com/content/2/843820Trigonometric convolution operatorsDiscrete analoguesComparisonStability inequalities
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Nessel RJ Röpsch C
spellingShingle	Nessel RJ Röpsch C On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions Journal of Inequalities and Applications Trigonometric convolution operators Discrete analogues Comparison Stability inequalities
author_facet	Nessel RJ Röpsch C
author_sort	Nessel RJ
title	On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions
title_short	On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions
title_full	On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions
title_fullStr	On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions
title_full_unstemmed	On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions
title_sort	on the comparison of trigonometric convolution operators with their discrete analogues for riemann integrable functions
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1025-5834 1029-242X
publishDate	1998-01-01
description	<p/> <p>This note is concerned with a comparison of the approximation-theoretical behaviour of trigonometric convolution processes and their discrete analogues. To be more specific, for continuous functions it is a well-known fact that under suitable conditions the relevant uniform errors are indeed equivalent, apart from constants. It is the purpose of this note to extend the matter to the frame of Riemann integrable functions. To establish the comparison for the corresponding Riemann errors, essential use is made of appropriate stability inequalities.</p>
topic	Trigonometric convolution operators Discrete analogues Comparison Stability inequalities
url	http://www.journalofinequalitiesandapplications.com/content/2/843820
work_keys_str_mv	AT nesselrj onthecomparisonoftrigonometricconvolutionoperatorswiththeirdiscreteanaloguesforriemannintegrablefunctions AT r246pschc onthecomparisonoftrigonometricconvolutionoperatorswiththeirdiscreteanaloguesforriemannintegrablefunctions
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On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions

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