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### Wave kernel for the circle $S^1$ - Poisson Summation Formula

Question : How could I compute the (wave) kernel from the fact I have already found (wave) trace on unit circle? The definitions are related to the page $25$ of the following pdf. As the ...
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### Reference request for the focussing example

I was reading "From Rotating Needles to Stability of Waves: Emerging Connections between Combinatorics, Analysis, and PDE" by Terence Tao, which is a Notice of the American Mathematical Society Vol. ...
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### Parametrices for the wave equation on manifolds with boundary

I am trying to understand parametrices for the solution operator $G_t = \sin(t\Delta)/\Delta$ to the wave equation $$(\partial_{tt} + \Delta)u_t=0, ~~~~~~~ u_0 =0, ~~~~~~\partial_tu_0 = f$$ on a ...
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### Non interacting complex unit

How to work with two non interacting complex units say i and j. These two imaginary complex unit represent different quantities. For example i is for periodicity in theta and j is for frequency or ...
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### Any reference in absorbing boundary conditions for non-abelian gauge fields?

Is there any paper on absorbing boundary conditions for non-abelian gauge fields? Currently I only saw some on elastic wave equations and some on EM fields.
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### Generalized wave equation

I asked this question here: http://math.stackexchange.com/questions/1160134/generalized-wave-equation but did not get any response. I hope it is more suitable on mathoverflow. I am interested in ...