  We investigate dispersive estimates for the Schr\"odinger operator $H=-\Delta
+V$ with $V$ is a real-valued decaying potential when there are zero energy
resonances and eigenvalues in four spatial dimensions. If there is a zero
energy obstruction, we establish the low-energy expansion $$
  e^{itH}\chi(H) P_{ac}(H)=O(1/(\log t)) A_0+
  O(1/t)A_1+O((t\log t)^{-1})A_2+ O(t^{-1}(\log t)^{-2})A_3. $$ Here
$A_0,A_1:L^1(\mathbb R^n)\to L^\infty (\mathbb R^n)$, while $A_2,A_3$ are
operators between logarithmically weighted spaces, with $A_0,A_1,A_2$ finite
rank operators, further the operators are independent of time. We show that
similar expansions are valid for the solution operators to Klein-Gordon and
wave equations. Finally, we show that under certain orthogonality conditions,
if there is a zero energy eigenvalue one can recover the $|t|^{-2}$ bound as an
operator from $L^1\to L^\infty$. Hence, recovering the same dispersive bound as
the free evolution in spite of the zero energy eigenvalue.
