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The Lebesgue Constants for Regular Hausdorff Methods

Published online by Cambridge University Press:  20 November 2018

Lee Lorch  and
Donald J. Newman
Lee Lorch
Affiliation:
University of Alberta
Donald J. Newman
Affiliation:
Yeshiva University
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The unboundedness of the sequence of Lebesgue constants (norms), at a point, of certain transforms implies, as is well known, that there exist (i) a continuous function whose transform fails to converge to the function at the point in question (the du Bois-Reymond singularity), and (ii) another such function whose transform, while converging everywhere to the function, does not do so uniformly in any neighbourhood of the stipulated point (the Lebesgue singularity). The converses also hold in our case.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 283 - 298
Copyright
Copyright © Canadian Mathematical Society 1961

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