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I am a mathematician, and recently got interested in the problem of compression of multi-dimensional functions. Particularly, there is a large piece of theory developed for fast computations with Newton potential [itex]\frac{1}{\|x-y\|}[/itex], where [itex]x, y \in R^{d}[/itex], [itex] d\geq 3[/itex].

Is there any interest among physical community in computations involving any kind of oscillatory kernels for arbitrary large dimensions, e.g. [itex]\frac{exp(ik\|x-y\|)}{\|x-y\|}[/itex], where [itex]x, y \in R^{d}[/itex], [itex] d\geq 3[/itex]?

Thank you in advance,

M.

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# Multi-dimensional oscillatory potentials: where are they used

Can you offer guidance or do you also need help?

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