Sampling in the Functional Hilbert Space

This work focuses on the study of sampling formulas for the range space H of a linear transform defined on a Hilbert space by means of a suitable kernel. The sampling property consists of the reconstruction of any func-tion inH through its values on an appropriate sequence of points by means of a sampling expansion involving these values. In our case, the sampling property is derived by assuming some requirements on the kernel of the linear transform. A converse result shows the generality of the required conditions in the Riesz bases setting. Finally, we deal with sampling formulas in the case where samples of a related function, the derivative for instance, are allowed in order to recover the initial function