Let $f$ be a complex valued function of $GL_n(\mathbb{A})$, where $\mathbb{A}$ is the adeles of some number field. Assume $f(ug)=\psi(u)f(g)$ for any $u$ in the standard maximal unipotent subgroup $N_n(\mathbb{A})$. If the integral $\int_{N_m(\mathbb{A})\backslash GL_m(\mathbb{A})}f(h)W_\phi(h) \; d h=0$ for any automorphic form $\phi$ on $GL_m$ and $W_\phi$ is the corresponding Whittaker function (here we embed $GL_m$ into $GL_n$ on the left upper corner), can we say $f$ is identically zero?

It is known that the corresponding local statement is true.