ИСТИНА

In noncommutative harmanic analysis there are many explicit integral transformation, which can be considered as higher analogs of Fourier transform. By our conjecture, they usually admit operational calculus. The images of certain natural differental operators of first order are differential-difference operators, usually they include differentiations of high order and difference operators include shift in imaginary direction as $f(x)\mapsto f(x+i)$, where $i^2=-1$, and $f\in L^2({\mathbb R})$. Now it is known a zoo of solved problems of this type, the simplest are the Fourier transform on the group $GL(2,{\mathbb R})$ and the Forier transform on Lobachevski plane. The most advanced known statement corresponds to restrictions from $\GL(n,\mathbb{C})$ to $GL(n-1, \mathbb{C})$.