Generalized Fourier Transforms Arising from the Enveloping Algebras of ๐ฐ๐ฉ(2) and ๐ฌ๐ฐ๐ญ(1โฃ2)
Generalized Fourier Transforms Arising from the Enveloping Algebras of ๐ฐ๐ฉ(2) and ๐ฌ๐ฐ๐ญ(1โฃ2)
The Howe dual pair |$(\mathfrak {sl}(2),O(m))$| allows the characterization of the classical Fourier transform (FT) on the space of rapidly decreasing functions as the exponential of a well-chosen element of |$\mathfrak {sl}(2)$| such that the Helmholtz relations are satisfied. In this paper, we first investigate what happens when instead we โฆ