Timeline for complex fourier coefficients, introduced by?
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2021 at 13:46 | vote | accept | nareto | ||
| May 30, 2012 at 17:38 | comment | added | roy smith | Of course a special case of a Fourier series in complex notation, the one for the theta function, the fundamental solution of the heat equation, was given by Jacobi in 1829 and generalized by Riemann in the 1850's. | |
| May 29, 2012 at 14:35 | answer | added | Jeff McGowan | timeline score: 3 | |
| May 28, 2012 at 16:08 | answer | added | Francois Ziegler | timeline score: 13 | |
| May 27, 2012 at 20:07 | comment | added | Alison Miller | The engineer you are thinking of might be Charles Steinmetz, who was known for introducing complex numbers to electrical engineering (specifically the study of alternating currents). However I can't find any evidence that he wrote general Fourier series in terms of complex exponentials. | |
| Apr 13, 2012 at 4:58 | answer | added | Paul B | timeline score: 11 | |
| Apr 7, 2012 at 1:09 | answer | added | Papiro | timeline score: 34 | |
| Mar 13, 2011 at 23:01 | comment | added | KConrad | Actually, maybe there are no complex Fourier series in the papers by Riesz or Fischer; one could imagine their theorem being about L^2-spaces of real-valued functions. So someone should check their papers to see what's in them. | |
| Mar 13, 2011 at 22:29 | comment | added | KConrad | The Riesz--Fischer theorem (1907) on the L^2-properties of Fourier series is a result where the complex exponential form of Fourier series is an essential ingredient. I don't have access to their paper, but on account of it I would guess that a systematic use of complex exponentials in Fourier series came no later than 1907. | |
| Mar 13, 2011 at 22:04 | comment | added | Mariano Suárez-Álvarez | (One can get scans of the book from archive.org; it is amazingly readable!) | |
| Mar 13, 2011 at 21:55 | comment | added | Mariano Suárez-Álvarez | I ave just spent a few minutes browsing Fourier's Traité de la chaleu, and I have to say I am quite surprised that I did not find any trigonometric series written in the exponential form. He is of course well aware of Euler's formula---he uses it several times---but he seems not to be moved to write Fourier series using it. It would be simply extraordinary if this had had to wait for the 1900s though! | |
| Mar 13, 2011 at 21:05 | comment | added | nareto | ok, edited the question | |
| Mar 13, 2011 at 21:05 | history | edited | nareto | CC BY-SA 2.5 |
added 376 characters in body
|
| Mar 13, 2011 at 14:29 | comment | added | Todd Trimble | I'm not sure I understand the question. Is the question something like: when did the Fourier representation of a (say real-valued) function in terms of complex exponentials come to predominate over the representation in terms of sines and cosines? I am having trouble believing it was really an engineer in 1900 who first introduced this, but it would be interesting to know more of the history, and how it might have led to the introduction of inner product spaces, Hilbert space, etc. (I'm also conflicted as to the appropriateness of this question for MO. Anyway, please clarify the question.) | |
| Mar 13, 2011 at 11:07 | history | asked | nareto | CC BY-SA 2.5 |