Steinmetz, Laplace and Fourier Transforms - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T09:57:38Z http://mathoverflow.net/feeds/question/98296 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/98296/steinmetz-laplace-and-fourier-transforms Steinmetz, Laplace and Fourier Transforms PaPiro 2012-05-29T18:33:57Z 2012-06-04T21:10:58Z <p>I am looking for references on <a href="http://en.wikipedia.org/wiki/Charles_Proteus_Steinmetz" rel="nofollow">Steinmetz</a> Transform and its relation with Laplace and Fourier Transforms. There is an <a href="http://it.wikipedia.org/wiki/Trasformata_di_Steinmetz" rel="nofollow">Italian Wikipedia</a> page about this topic but with no references.</p> http://mathoverflow.net/questions/98296/steinmetz-laplace-and-fourier-transforms/98813#98813 Answer by Francois Ziegler for Steinmetz, Laplace and Fourier Transforms Francois Ziegler 2012-06-04T21:10:58Z 2012-06-04T21:10:58Z <p>(Too long for a comment.) I think the italian Wiki page is wrong. It says the transform "was conceived by the author in 1893 [probably <em><a href="http://archive.org/stream/proceedingsinte02chicgoog#page/n66" rel="nofollow">this text</a></em>] and exposed in his treatise <em><a href="http://archive.org/stream/theorycalculation00steirich" rel="nofollow">Theory and Calculation of Alternating Current Phenomena</a></em> four years later."</p> <p>However, as you can check there is not a trace in these texts (nor in the others authored by Steinmetz and available on archive.org) of what Wikipedia calls "la transformata di Steinmetz" -- i.e. the Fourier isomorphism $L^2(S^1)\to\ell^2(\mathbf{Z})$ -- which by the way, was written explicitly <a href="http://mathoverflow.net/questions/58325/complex-fourier-coefficients-introduced-by/" rel="nofollow">much before 1893</a>.</p> <p>These texts are famous for introducing complex numbers (in particular the notation $j=\sqrt{-1}$) into electrical engineering, but my impression is that naming the transform in Steinmetz's honor happened much later, perhaps in Italy, with little regard to what he himself actually did (or as the case may be, never did) with it.</p>