(A)dS Holography with a Cut-off

Abstract: We find out the smearing/ transfer functions that relate a local bulk operator with its boundary values at a cut-off surface located at $z=z_0$ of the AdS Poincar\'{e} patch. We compare these results with de Sitter counterparts and comment on their connections with corresponding construction for dS/ CFT. As the boundary values can help define the required field theory at $z=z_0$ and encode bulk locality in terms of it, our work can provide key information about holographic RG in the context of AdS/ CFT.