Superdense a.e. Unbounded Devergence in Some Approximation Processes of Analysis
S. Cobzaş and I. Muntean
Source: Real Anal. Exchange Volume 25, Number 2
(1999), 501-512.
Abstract
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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Keywords: Banach-Steinhaus principle; condensation of singularities; generic divergence results for Lagrange interpolation; Fourier series; Walsh-Fourier series
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rae/1230995389
Mathematical Reviews number (MathSciNet): MR1778508
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