Koshliakov kernel and identities involving the Riemann zeta function

Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions $J_z(x),Y_z(x)$ and $K_z(x)$ are studied. Interesting special cases of these identities are derived, one of which is connected to a well-known transformation due to Ramanujan, and Guinand.