Non-Gaussian analysis and hypergroups (Q1916670)

The authors consider a broad class of hypergroups \(H_f\) including, in particular, the following hypergroups: 1) \(H_f\) is the group algebra of the group \(R\); 2) \(H_f\) is generated by the Sturm-Liouville expression on the semiaxis; 3) \(H_f\) is generated by the generalized translation operator on the semiaxis. -- It is shown in the article that the approach to the generalization of Gaussian infinite-dimensional analysis (white noise analysis) which is based on biorthogonal expansions can be extensively generalized on the hypergroups \(H_f\).