r-norm bounds and metric properties for zero loci of real analytic functions

We consider the problem of deciding whether or not a zero locus, X, of multivariate real analytic functions crosses a given r-norm ball in the real n-dimensional affine space. We perform a local study of the problem, and we provide both necessary and sufficient conditions to answer the question. Our conditions derive from the analysis of differential geometric properties of X at the center of the ball. An algorithm to evaluate r-norms distances is proposed

r-norm bounds and metric properties for zero loci of real analytic functions

We consider the problem of deciding whether or not a zero locus, X, of multivariate real analytic functions crosses a given r-norm ball in the real n-dimensional affine space. We perform a local study of the problem, and we provide both necessary and sufficient conditions to answer the question. Our conditions derive from the analysis of differential geometric properties of X at the center of the ball. An algorithm to evaluate r-norms distances is proposed.Ministerio de Economía y CompetitividadEuropean Regional Development FundA major part of this work was developed while J.R. Sendra was visiting, in the frame of GNSAGA—Istituto Nazionale di Alta Matematica, the University of Genova, and while M.C. Beltrametti and M. Torrente were visiting the University of Alcalá, in the frame of the project Giner de los Rios and of GNSAGA—Istituto Nazionale di Alta Matematica

Corrigendum for "Almost vanishing polynomials and an application to the Hough transform"

In this note we correct a technical error occurred in [M. Torrente and M.C. Beltrametti, "Almost vanishing polynomials and an application to the Hough transform", J. Algebra Appl. 13(8), (2014)]. This affects the bounds given in that paper, even though the structure and the logic of all proofs remain fully unchanged.Comment: 30 page