Reproducing kernel structure and sampling on time-warped Kramer spaces

Given a signal space of functions on the real line, a time-warped signal space consists of all signals that can be formed by composition of signals in the original space with an invertible real-valued function. Clark´s (1985) theorem shows that signals formed by warping bandlimited signals admit formulae for reconstruction from samples. This paper considers time warping of more general signal spaces in which Kramer´s (1959) generalized sampling theorem applies and observes that such spaces admit sampling and reconstruction formulae. This observation motivates the question of whether Kramer´s theorem applies directly to the warped space, which is answered affirmatively by introduction of a suitable reproducing kernel Hilbert space structure. This result generalizes one of Zeevi (1993), who pointed out that Clark´s theorem is a consequence of Kramer´s