For reasons well known in KAM theory, when solving the linear cohomological equation over a Diophantine rotation, one has to introduce an infrared cut-off \( T_{N} \), projecting on frequencies lower than \( N\), and an ultraviolet cut-off \( R_{N} \), projecting on frequencies strictly higher than \( N\).
These operators can be easily estimated in the relevant norm by applying Johnson's cut-off theorem, proved in [Co98].
Since, however, we know by construction that
Corollary 1. The visible spectrum is empty. If you publish too much in KAM, you will go blind.
These operators can be easily estimated in the relevant norm by applying Johnson's cut-off theorem, proved in [Co98].
Since, however, we know by construction that
\( T_{N} + R_{N} = \mathrm{Id} \)
we obtain immediately the following corollary.Corollary 1. The visible spectrum is empty. If you publish too much in KAM, you will go blind.
