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Subdivision schemes are iterative methods for the design of smooth curves andsurfaces. Any linear subdivision scheme can be identified by a sequence ofLaurent polynomials, also called subdivision symbols, which describe the linearrules determining successive refinements of coarse initial meshes. Oneimportant property of subdivision schemes is their capability of exactlyreproducing in the limit specific types of functions from which the data issampled. Indeed, this property is linked to the approximation order of thescheme and to its regularity. When the capability of reproducing polynomials isrequired, it is possible to define a family of subdivision schemes that allowsto meet various demands for balancing approximation order, regularity andsupport size. The members of this family are known in the literature with thename of pseudo-splines. In case reproduction of exponential polynomials insteadof polynomials is requested, the resulting family turns out to be thenon-stationary counterpart of the one of pseudo-splines, that we here call thefamily of exponential pseudo-splines. The goal of this work is to derive theexplicit expressions of the subdivision symbols of exponential pseudo-splinesand to study their symmetry properties as well as their convergence andregularity.

Exponential Splines and Pseudo-Splines: Generation versus reproduction of exponential polynomials