In standard spectral multiplier theorems the critical index is determined by dimension of the corresponding semigroup. If we consider elliptic operators this dimension usually coincides with the Euclidean dimension of underlying space. However for sub-elliptic operator the dimension of the corresponding semigroup is strictly greater than Euclidean dimension of underlying space. Together with Michael Cowling we proved a Hörmander type spectral multiplier theorem for a sub Laplacian on ${\rm SU}(2)$ with the critical exponent equal to half the Euclidean dimension of the group. This is an analogue of the result obtained by Hebisch , Müller and Stein for the Heisenberg group. The group ${\rm SU}(2)$ is the only example of a simple Lie group for which such precise spectral multiplier theorems have been proved. This result is an important contribution to our understanding of sub-elliptic operators. We also developed techniques of proving very precise multiplier results for operators with finite speed propagation of the corresponding wave equation.