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1999/2000 Superdense a.e. Unbounded Devergence in Some Approximation Processes of Analysis
S. Cobzaş, I. Muntean
Real Anal. Exchange 25(2): 501-512 (1999/2000).


The paper deals with divergence phenomena for various approximation processes of analysis such as Fourier series, Lagrange interpolation, Walsh-Fourier series. We prove the existence of superdense (meaning residual, dense and uncountable) families of functions in appropriate function spaces over an interval $T\subset \mathbb R.$ One proves that for each function in the family, the corresponding approximation process is unboundedly divergent on a superdense subset of $T$ of full measure.


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S. Cobzaş. I. Muntean. "Superdense a.e. Unbounded Devergence in Some Approximation Processes of Analysis." Real Anal. Exchange 25 (2) 501 - 512, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 3 January 2009

zbMATH: 1215.41009
MathSciNet: MR1778508

Primary: 41A65 , 46B99

Keywords: Banach-Steinhaus principle , condensation of singularities , Fourier series , generic divergence results for Lagrange interpolation , Walsh-Fourier series

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 2 • 1999/2000
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