Talk:Wave front set

If s.o. wants to delete "the notion of" from the intro, maybe some more care should be taken to precise that &xi; must be nonzero in order to belong to &Sigma; (i.e. add "&xi;=0 or" after \iff)... &mdash; MFH: Talk 23:44, 25 May 2005 (UTC)


 * (DONE)  &mdash; MFH: Talk

unprecise precisions
Dear C.M.,

thanks for putting the [ [ ... ] ] at the right place (cotangent bundle vs WF set). However, I'm not so happy about your other edits, and rather prefer the old version:
 * 'direction' is a bit misleading, because the Fourier transform is about frequency (i.e. roughness) and not spatial direction. And, I think at this quite ealy point of the article, such a precision is not yet needed and rather tears apart the 'preface'. (Which, I admit, is not obvious as I did not "start" the article with an ==introduction== or ==history== section.) However, your point about dimension > 1 is worth mentioning. Maybe we should duplicate this, and put your developed version in a separate paragraph, leaving my short version in the 'preface'.
 * I can't see why you put the miniscule T*(X) into a 'displayed' equation. Well, I can imagine: you choose to display all math tags as PNG. But this is your choice, not the standard setting, and I feel it's not justified.

On both points, I'm quite tempted to put back the original version. Would you mind very much? &mdash; MFH: Talk 12:44, 26 May 2005 (UTC)

Direction: it is how I think of microlocal, somehow. That is, local analysis which is like localisation in algebra, or inverting operators, has to be supplemented by something talking about directions at a point. The cotangent 'directions' are available to talk about, and the Fourier interpretation is just one way of looking at that. Well, I suppose I am just discussing my own intuitions. General ideas of this kind really belong at the level of introduction to the microlocal analysis article; which is yet to be written.

Format: at present the consensus seems to be MathHTML for inline formulae. I don't feel it is harmful to display more formulae: it makes a page less dense to read.

Charles Matthews 14:47, 26 May 2005 (UTC)

Geometric Asymptotics by Gullemin and Sternberg, Ch. VI Geometric Aspects of Distributions, introductory paragraph, contains this:


 *  ... the notion of the wave front set, a subset of the cotangent bundle, which measures the singular codirections for distributions.

Charles Matthews 15:46, 27 May 2005 (UTC)

Thanks for recalling the notion of codirection which I did not think of and thus did not mention in my article, which definitely is far from being complete. So I reiterate what I already suggested:
 * However, your point about dimension > 1 is worth mentioning. Maybe we should duplicate this, and put your developed version in a separate paragraph, leaving my short version in the 'preface'.

&mdash; MFH: Talk 18:34, 27 May 2005 (UTC)

Typo
Just to point that there is 2 different choice of functions "phi" in the formal definition ( in tex this would be \phi and \varphi but I don't do math in html) so please fix: First reference to test function is used with \phi second one is typed outside math env. and doesn't not look at all the same (phi(x_0) not 0)