The Zero-Removing Property in Hilbert Spaces of Entire Functions Arising in Sampling Theory

In the topic of sampling in reproducing kernel Hilbert spaces, sampling in Paley-Wiener spaces is the paradigmatic example. A natural generalization of Paley-Wiener spaces is obtained by substituting the Fourier kernel with an analytic Hilbert-space-valued kernel K. Thus we obtain a reproducing kernel Hilbert space H-K of entire functions in which the Kramer property allows to prove a sampling theorem. A necessary and sufficient condition ensuring that this sampling formula can be written as a Lagrange-type interpolation series concerns the stability under removal of a finite number of zeros of the functions belonging to the space H-K; this is the so-called zero-removing property. This work is devoted to the study of the zero-removing property in H-K spaces, regardless of the Kramer property, revealing its connections with other mathematical fields.

The Zero-Removing Property in Hilbert Spaces of Entire Functions Arising in Sampling Theory Articles