Growth of Weyl coefficient and monodromy matrix of a canonical system

For two-dimensional canonical systems of differential equations, we investigate the growth of analytic functions encoding the spectrum. We give two-sided estimates for the values along the imaginary axis of

• the imaginary part of the Weyl coefficient (in limit point case)
• an entry of the monodromy matrix (in limit circle case).

These estimates let us determine whether a given function is integrable with respect to the spectral measure, give bounds for the eigenvalue counting function, and characterize membership of resolvents in a Schatten–von Neumann class with small index (most notably trace class).