Water waves, mathematics & computation

Fourier Multipliers as Operators Fourier analysis is especially useful for linear, translation-invariant operators. In physical space, such an operator may involve derivatives…

In a Green's function \(G(x,x')\), the primed variable \(x'\) marks the source point — the location of a unit impulse — while \(x\) is the field point where the response is…

浓雾氤氲的森林，分不清是清晨还是黄昏，天边应该是有丝丝破碎的晨曦亦或是夕阳，还未走进你眼眸，便融化进了昏霭，染成一片模糊的光晕。你的思绪也仿若虚无之地，白茫茫一片，犹豫，抬起脚，犹豫，犹豫，犹豫，向前？向后？是追忆还是邂逅迷茫？

We show how the spectral relation ∑ Formula implies the physical-space operator identity ∑ Formula, by inverse Fourier transform and the commutation of \(\partial_z\) with the hori…

The math is sound. The method is not. We show that the order- \(n\) Hankel transform in \(r\) diagonalizes the Bessel-type radial operator \(\mathscr{L}_n\), mapping the PDE…