**S.K. Ray**

Indian Statistical Institute, Kolkata

April 19, 2012

**Fourier restriction theorem on Riemannian symmetric spaces of noncompact type**:
Restriction conjecture on $\mathbb R^n$ asks for the validity of
an inequality of the form $\|\hat{f}\mid S^{n-1}\|_{L^q(S^{n-1})}\leq
c_{p,q}\|f\|_{L^p(\mathbb R^n)}$ for all Schwartz functions on $\mathbb R^n$. Here $\hat{f}$ denotes the Euclidean Fourier transform of $f$ and $c_{p,q}>0$ is a constant independent of $f$. After introducing the problem on $\mathbb R^n$ we will talk about an analogue of the above inequality on Riemannian symmetric spaces of noncompact type having rank one. We will show that problem is related to the estimates of the matrix entries of the spherical principal series representation and hence to the Kunze Stein phenomena.