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Suppose $f \in C^{\infty}_c((-1,1))$ and assume that there exists constants $a,b>0$ such that $$ \bigg|\int_{\mathbb R} f(t) \,e^{\tau t^2+i\tau t}\,dt\bigg| \leq a\,e^{-b|\tau|},$$ for all $\tau \...

I have found some functions $t_g, g \in G$ for cyclic groups $G=C_n$ which seem to satisfy the following convolution identity: $$t_g(x+y) = \sum_{h \in G} t_{gh^{-1}}(x) t_h(y)$$ Example of such ...