Donoho–Stark and Paley–Wiener theorems for the G-transform

This paper deals with a class of G-transformsg(x)=G(f)(x):=∫0∞G2n,2mm,n(xy|(an),−(a¯n)(bm),−(b¯m))f(y)dy with the Meijer G-function as the kernel. We prove the Donoho–Stark uncertainty principle for the G  -transform. We also give a characterization of the image of functions that have compact support (Paley–Wiener type theorem) under this class of transforms in case n=0n=0.