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 Jz(x)Jz(x), Yz(x)Yz(x) and Kz(x)Kz(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.