  We introduce an alternate yet a simple Fokas method (aka UTM) based approach
for proving the interior-boundary Strichartz estimate for solutions of the
initial boundary value problem (ibvp) for the Schr\"odinger equation posed on
the right half line. We utilize the solution representation formula obtained
through the Fokas method and a few basic tools from the oscillatory integral
theory. Representation formula for solutions of the ibvp splits into two parts,
one of which is analyzed via the theory of oscillatory integrals, whereas the
second part nicely transforms, via a time-to-space switch, into a Cauchy
problem for which Strichartz estimates are already known. The obtained estimate
implies the local wellposedness of low regularity solutions for the associated
nonlinear ibvp, which was previously treated by other powerful however
technical methods. We in particular extend the recent Fokas method based
$L_t^\infty H_x^s(\mathbb{R}_+)$ estimates to Fokas method based $L_t^\lambda
W_x^{s,r}(\mathbb{R}_+)$ estimates for any admissible pair $(\lambda,r)$. This
implies that UTM formulas are capable of defining weak solutions of NLS also
below the Banach algebra threshold $C_tH_x^\frac{1}{2}(\mathbb{R}_+)$. The
approach is uniform and can be easily extended to a large class of ibvps and
boundary values associated with dispersive equations, this is all thanks to the
nice oscillatory kernels of the associated representation formulas. In
particular, Strichartz estimates for the Neumann problem are new here.
