On recognition of the finite simple orthogonal groups of dimension $2^m$, $2^m+1$ and $2^m+2$ over a field of characteristic 2

The spectrum $\omega(G)$ of a finite group $G$ is the set of element orders of $G$. A finite group $G$ is said to be recognizable by spectrum (briefly, recognizable) if $H\simeq G$ for every finite group $H$ such that $\omega(H)=\omega(G)$. We give two series, infinite by dimension, of finite simple classical groups recognizable by spectrum.