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A new class of univariate stationary interpolatory subdivision schemes of dual type is presented. As opposed to classical primal interpolatory schemes, these new schemes have masks with an even number of elements and are not step-wise interpolants. A complete algebraic characterization, which covers every arity, is given in terms of identities of trigonometric polynomials associated to the schemes. This characterization is based on a necessary condition for refinable functions to have prescribed values at the nodes of a uniform lattice, as a consequence of the Poisson summation formula. A strategy for the construction is then showed, alongside meaningful examples for applications that have comparable or even superior properties, in terms of regularity, length of the support and/or polynomial reproduction, with respect to the primal counterparts.
The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of certain asso
In this paper, we present a family of multivariate grid transfer operators appropriate for anisotropic multigrid methods. Our grid transfer operators are derived from a new family of anisotropic interpolatory subdivision schemes. We study the minimal
Positive interpolatory cubature formulas (CFs) are constructed for quite general integration domains and weight functions. These CFs are exact for general vector spaces of continuous real-valued functions that contain constants. At the same time, the
Lagrange functions are localized bases that have many applications in signal processing and data approximation. Their structure and fast decay make them excellent tools for constructing approximations. Here, we propose perturbations of Lagrange funct
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functi