  We consider a planar waveguide with "twisted" boundary conditions. By
twisting we mean a special combination of Dirichlet and Neumann boundary
conditions. Assuming that the width of the waveguide goes to zero, we identify
the effective (limiting) operator as the width of the waveguide tends to zero,
establish the uniform resolvent convergence in various possible operator norms,
and give the estimates for the rates of convergence. We show that studying the
resolvent convergence can be treated as a certain threshold effect and we
present an elegant technique which justifies such point of view.
