$f(x)$ is $C^1$. Let interval $I = [0, 2\pi]$ and $I = I_1\cup I_2, I_1\cap I_2 = \emptyset$. Now suppose that $f(x) \equiv 0, \forall x\in I_1$ and the convolution $g(x) = \int_0^{2\pi}f(t)\cot((x-t)/2)\,dt \equiv 0,\forall x\in I_2$. Can we prove that $f(x)\equiv 0, \forall x\in I$ or find a counterexample?
2026-04-06 18:55:18.1775501718
Convolution with Cotangent function
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