Abstract
We know from Chap. 3 that any piecewise continuous periodic function f(x) can be expanded into a Fourier series.
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- 1.
In the following, references to the first volume of this course (L. Kantorovich, Mathematics for natural scientists: fundamentals and basics, Springer, 2015) will be made by appending the Roman number I in front of the reference, e.g. Sect. I.1.8 or Eq. (I.5.18) refer to Sect. 1.8 and Eq. (5.18) of the first volume, respectively.
- 2.
This assumption is in fact not necessary and Eq. ( 5.16) can be proven without it. However, this will not be done here as it would lead us to a much lengthier calculation.
- 3.
The case with the memory will be considered in Sect. 6.5.2
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Kantorovich, L. (2016). Fourier Transform. In: Mathematics for Natural Scientists II. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-27861-2_5
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DOI: https://doi.org/10.1007/978-3-319-27861-2_5
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