given the operator
$ P_{\Lambda } = (f\in L^{2}(R)^{even}| f(q)=0 , |q| \ge \Lambda) $
what does it mean? the operator $ P_{\Lambda} $ acts over a function $f(q) $ by setting this (even) function to zero whenever $ |q| \ge \Lambda $
how could i evaluate its Eigenvalues and Eigenfunctions ?? thanks
$ P_{\Lambda} T_{n}= \mu _{n} T_{n} $ , can we have a mening to $ P_{\Lambda}^{k} $ ? its power iteration, does this operator have a geommetric meaning ?