7 problems

Let $N\in\mathbb{N}$, $a>0$, and let $\Delta_k$ denote the Dunkl Laplacian. Define $\mathcal{S}_{k,a}(\mathbb{R}^N)$ as the space of all functions…

Arbitrary-dimensional product formula conjecture. The above product formulae should hold for arbitrary dimensions when $a=\frac{2}{n}$ with $n\in\mathbb{N}_+$.

Let $\alpha\geq -1/2$, $p\in(1,\infty)$, and let $w\colon\mathbb{R}\to[0,\infty)$ satisfy … where the supremum is over all intervals $B\subset\mathbb{R}$ and $1/p+1/p'=1$. The weig…

The $(\kappa,a)$-generalized Fourier transform has Schwartz distribution kernel $B_{\kappa,a}(x,y)$, where $\kappa$ is a multiplicity function, $a$ is the deformation parameter,…

Weyl-invariant Dunkl Newton-kernel conjecture. For $X,Y\in\overline{\mathfrak{a}^+}$ and $d\geq3$, one has

Spherical-function growth conjecture. If $\lambda,X\in\overline{\mathfrak{a}^+}$, then

Potential-kernel conjecture. For $x\in B^+$ and $y\in S^+$,