Continuous Gabor transform for strong hypergroups
On every commutative hygergroup, one can define a generalized translation operator and a generalized Haar measure; thus, it is natural to extend the classical results from Gabor analysis to this setting. With the definition of the continuous Gabor transform given in the paper, the authors obtain generalizations of the main results in Gabor analysis, e.g., the Plancherel formula and the inversion formula. The results are applied to Bessel-Kingman hypergroups and to the dual Jacobi polynomial hypergroups.
scientific article; zbMATH DE number 2018212