On Nonintersection of Spectra of some Functionals on Spaces $\stackrel{\circ }{<mi>W</mi>}{}_n^2$, $\stackrel{\circ }{<mi>W</mi>}{}_{n+1}^2$, $\stackrel{\circ }{<mi>W</mi>}{}_{n+2}^2$

Spectra of functionals $$\mathrm{\Phi }(u)=\frac{⟨u^{(n)}{u}^{(n)}⟩}{⟨u^{(n-p)}{u}^{(n-p)}⟩}$$ in spaces ${\stackrel{\circ }{}}_n^2$ are considered for different $n$. One has shown that for even functions in $\stackrel{\circ }{}{}_n^2$ and $\stackrel{\circ }{}{}_m^2$ spectra of functionals do not intersect for $m=n+1,n+2$. The neccesary conditions for two spectra to intersect are written for $\mathrm{\Delta }=m-n>2$.