Timeline for An invariant method of stationary phase
Current License: CC BY-SA 3.0
11 events
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| Oct 17, 2016 at 15:31 | comment | added | Matthias Ludewig | Given $p \in C$, to calculate $(u/H\phi)_p[v_1, \dots, v_k]$ (where we ay assume that $v_1, \dots, v_k \in T_pC$ are linearly independent, choose vectors $b_1, \dots, b_{n-k}$ that complement $v_1, \dots, v_k$ to a basis of $T_p M$ (i.e. such that their projections $[b_1], \dots, [b_{n-k}]$ form a basis of $T_pM/T_pC$. Then define $(u/H\phi)_p[v_1, \dots, v_k := u_p[v_1, \dots, v_k, b_1, \dots, b_{n-k}]/H\phi[b_1, \dots, b_{n-k}]$. It is easy to check that this definition is independent from the choice of $b_1, \dots, b_{n-k}$. | |
| Oct 14, 2016 at 18:12 | comment | added | B K | In my research, I am still dealing with a similar question. Therefore, I am interested to know what you mean with the quotient u/H\phi. I can't see how this should be understood correctly so that it defines a k-density on C. In other words, what is (u/H\phi)|_p[v_1,...,v_k] for k vectors v_i in the tangent space of C at some point p in C? | |
| Nov 13, 2015 at 8:32 | comment | added | Matthias Ludewig | No, sadly not, but I didn't have the time to really think about it longer... | |
| Nov 12, 2015 at 14:52 | comment | added | B K | Matthias, have you been able to figure out a useful answer to this question since 2012? While I am very interested in this, I don't know an appropriate reference either. | |
| Nov 28, 2012 at 8:41 | history | edited | Denis Serre | CC BY-SA 3.0 |
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| Nov 27, 2012 at 21:41 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
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| Nov 27, 2012 at 21:31 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
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| Nov 27, 2012 at 21:05 | answer | added | Bazin | timeline score: 1 | |
| Nov 27, 2012 at 21:03 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
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| Nov 27, 2012 at 20:28 | answer | added | Liviu Nicolaescu | timeline score: 2 | |
| Nov 27, 2012 at 19:55 | history | asked | Matthias Ludewig | CC BY-SA 3.0 |