Talk:42-XX

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The name `Fourier analysis' does not reflect the current terminology, name changed per ALD's request. DAC 08:20, 23 November 2007 (PST)

ALD and DAC feel that the two sections 42 and 43 should be combined into one section called Harmonic Analysis and the changes made in 42 reflect this idea. Regarding 43-XX Abstract Harmonic Analysis we suggest that it become part of 42-XX say 42Dxx with no other changes. That is, replace 43A with 42D wherever it appears. DAC 11:19, 7 December 2007 (PST)

Although it's clear that the subject of Harmonic Analysis as it is generally practiced nowadays grew out of classical Fourier Analysis and includes it, and much of the interest in is in non-classical topics, especially non-trigonometric bases and frames and generalizations to noncommutative situations, we already do have 42 as mainly classical Fourier analysis and 43 for the abstractions that are the more general harmonic analysis, especially for noncommuatitve groups. Thus it is not generally agreed that we should rename the sections as the above suggestion suggests. It is not clear what simplification or enhancement for the public users that change would bring (the public already knows to look at 42 + 43 if they are interested in 'the whole field'. In any case, it can be argued that the whole subject is really part of a more general representation theory, first for groups and their close relatives, but then perhaps for more general groupoids, or even tensor categories. PIon 20:09, 1 January 2008 (PST)