Bessel identities in the Waldspurger correspondence over the real numbers
In this paper certain identities between Bessel functions attached to irreducible unitary representations of \(\text{PGL}_2 (\mathbb R)\) and those for the double cover of \(\text{SL}_2 (\mathbb R)\) are established. Then a correspondence between such representations is realized by these Bessel identities, it is just the Waldspurger correspondence. Several regularity theorems for Bessel distributions appearing in the relative trace formula are proved by using a classical result of Weber and Hardy on Fourier transforms of classical Bessel functions. This paper constitutes the local (real) spectral theory of the relative trace formula for the Waldspurger correspondence for which the global part was developed by Jacquet.
scientific article; zbMATH DE number 2164534
scientific article