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I am not sure that this question is research level, but it was not answered at MSE for several days, so I place it here. I am interested in a quantitative version of the principle that smoothness of ...

The uniqueness of Radon transform can be expressed by the following claim (I assumed that the function has compact support for simplicity): If a continuous function with compact support has zero ...

Quart. J. Math. Volume 37, Issue 1, Pages 53-79 On double Fourier series, and especially those which represent the double zeta-function with real and incommensurable parameters. Hardy, G.H. I am not ...

Let $f$ and $g$ be two functions defined over the 2d sphere $\mathbb{S}^2$. The convolution between $f$ and $g$ is defined as a function $f * g$ over the space $SO(3)$ of 3d rotations as $$(f*g)(R) = \...

Upon looking at the graphs of various Fourier sine and cosine transforms (ones without Dirac deltas in their domain) I've noticed a pattern that is probably already known, but that I thought would be ...

I am completely stuck on a comparison between $f(t)^2$ and $\hat{f}(t)^2$ in an integral. Considering $f(t)$ of rapid decrease at infinity such that near zero: $f(t) \sim_0 t^{-\frac{1}{2}- \alpha}+o(...