Smooth transfer of Kloosterman integrals (the Archimedean case)
Smooth transfer of Kloosterman integrals (the Archimedean case)
We establish the existence of a transfer, which is compatible with Kloosterman integrals, between Schwartz functions on ${\rm GL}_n(\Bbb{R})$ and Schwartz functions on the variety of non-degenerate Hermitian forms. Namely, we consider an integral of a Schwartz function on ${\rm GL}_n(\Bbb{R})$ along the orbits of the two sided action of …