On the kernel of the -Generalized fourier transform
On the kernel of the -Generalized fourier transform
Abstract For the kernel $B_{\kappa ,a}(x,y)$ of the $(\kappa ,a)$ -generalized Fourier transform $\mathcal {F}_{\kappa ,a}$ , acting in $L^{2}(\mathbb {R}^{d})$ with the weight $|x|^{a-2}v_{\kappa }(x)$ , where $v_{\kappa }$ is the Dunkl weight, we study the important question of when $\|B_{\kappa ,a}\|_{\infty }=B_{\kappa ,a}(0,0)=1$ . The positive answer was …