Multi-dimensional oscillatory potentials: where are they used

[mett_the_fish]

Hi,

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 $\frac{1}{\|x-y\|}$, where $x, y \in R^{d}$, $d\geq 3$.
Is there any interest among physical community in computations involving any kind of oscillatory kernels for arbitrary large dimensions, e.g. $\frac{exp(ik\|x-y\|)}{\|x-y\|}$, where $x, y \in R^{d}$, $d\geq 3$?

Thank you in advance,
M.

 

[eljose79]

Hello M.,

As a scientist working in the field of physics, I can say that there is definitely interest in computations involving oscillatory kernels for arbitrary large dimensions. In fact, oscillatory kernels have been used in various fields of physics, such as quantum mechanics, electromagnetism, and fluid dynamics, to name a few.

One specific example is in the study of wave propagation, where oscillatory kernels are used to model the behavior of waves in different media. In this context, the oscillatory nature of the kernel is crucial in accurately describing the behavior of the waves.

Additionally, in the field of signal processing, oscillatory kernels are used in Fourier analysis to decompose signals into their frequency components. This has applications in various areas such as image and audio compression, data compression, and data analysis.

Therefore, I would say that there is definitely interest in computations involving oscillatory kernels for arbitrary large dimensions in the physical community. I hope this helps in your research and exploration of this topic.