  Isolating cuspidal automorphic representations from the whole automorphic
spectrum is a basic problem in the trace formula approach. For example, matrix
coefficients of supercupidal representations can be used as test functions for
this, which kills the continuous spectrum, but also a large class of cuspidal
automorphic representations. For the case of number fields, multipliers of the
Schwartz algebra is used in the recent work [3] to isolate all cuspidal
spectrum which provide enough test functions and suitable for the comparison of
orbital integrals. These multipliers are then applied to the proof of the
Gan-Gross-Prasad conjecture for unitary groups [3,2]. In this article, we prove
similar result on isolating the cuspidal spectrum in [3] for the function field
case.
