Periodic function with the capacity of being $g'' = \lambda g$

82 Views Asked by At

Related to the question : Eigenvalues of the circle over the Laplacian operator, what kind of periodic chart $c:(-\pi,\pi)\rightarrow S^1$ has the property that for a continuous function $f$, $g :=f \circ c$ is periodic, and such that $g'' = \lambda g$ as in the Thomas's comment?