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  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 . 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.
|Title of host publication||Applied and Numerical Harmonic Analysis|
|Publisher||Springer International Publishing|
|Number of pages||17|
|State||Published - 2019|
|Name||Applied and Numerical Harmonic Analysis|
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