Transmutations from the Covariant Transform on the Heisenberg Group and an Extended Umbral Principle
Abstract
We discuss several seemingly assorted objects: the umbral calculus, generalised translations and associated transmutations, symbolic calculus of operators. The common framework for them is representations of the Weyl algebra of the Heisenberg group by ladder operators. Transporting various properties between different implementations we review some classic results and new opportunities.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.