I'm working on a problem that requires the following operator, $A^TA$, to have an orthonormal set of eigenfunctions.
Note $A:H_1 \mapsto H_2$, where $H_1$ and $H_2$ are separable Hilbert spaces. Furthermore, $A$ is also continuous, linear and injective. In addition, $A^T$ denotes the adjoint of $A$.
Could anyone point me towards a theorem or something that might help? Thanks.