Bounded variation and sampling

Elijah Liflyand

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this chapter, we shall consider certain problems where a function of bounded variation generates trigonometric series which are then compared with its Fourier integral. In fact, Chapter 4 in [198] is devoted to these problems. Here, the more modern term “sampling” is equivalent to the older “discretization”. Those who expected a sort of Whittaker–Kotel’nikov–Shannon type matter might be disappointed. The present chapter can be considered as a development of certain of the results in [198]. One type of these results, the Poisson summation formula, is old and classical. However, results related to bounded variation are specific and a bit off a field. The other one is more recent and aims to the comparison of Fourier integrals and trigonometric series related to functions and sequences with bounded variation.

Original languageEnglish
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Number of pages17
StatePublished - 2019

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.


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