Edmunds-Evans essential spectra of the generalized Constantin-Lax-Majda linearization

For $0<a<1$, we study the linearization $L_a$ about a smooth odd self-similar collapse profile $(Ω,c_l)$ of the generalized Constantin-Lax-Majda equation, where $c_l$ is the focusing exponent. On the origin-$H^2$ realization $X=\{φ\in L^2(0,\infty):φ(0)=0,φ''\in L^2(0,\infty)\}$, under explicit tran