The hermite transform: A survey

Abstract

With this survey on the Hermite transformation we want to pursuethe following two goals. First, we want to provide a comprehensiveand up-to-date description of the Hermite transformation, itsunderlying philosophy, and its most important propertiesand their implications for applications. As so oftenwhen publications and development go hand-in-hand, new insightshave led to changes in or generalizations of already publishedresults, and not all of these changes have been consideredsufficiently substantial to be published separately. As aconsequence, the existing publications on the Hermitetransformation do not fully reflect our most recent insights, andthe current paper intends to remedy this. Second, we also want toshare some new results. Two specific new results, that is, partialsignal decompositions and intersection curvatures, are thereforetreated in more detail than other aspects.