Sampling of band-limited vectors

Given a self-adjoint, positive definite operator on a Hilbert space the con cept of band-limited vectors (with a given band-width) is developed, using the spectral decomposition of that operator: By means of this concept suffi cient conditions on collections of linear functionals {phi (v)} are derived which imply that all band limited vectors in a given class are uniquely de termined resp, can be reconstructed in a stable way from the set of discret e values {phi (v) (f)}.