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dc.contributor.authorBerman, Robert J.-
dc.contributor.authorOrtega Cerdà, Joaquim-
dc.description.abstractWe consider the problem of stable sampling of multivariate real polynomials of large degree in a general framework where the polynomials are defined on an affine real algebraic variety $M$, equipped with a weighted measure. In particular, this framework contains the well-known setting of trigonometric polynomials (when $M$ is a torus equipped with its invariant measure), where the limit of large degree corresponds to a high frequency limit, as well as the classical setting of one-variable orthogonal algebraic polynomials (when $M$ is the real line equipped with a suitable measure), where the sampling nodes can be seen as generalizations of the zeros of the corresponding orthogonal polynomials. It is shown that a necessary condition for sampling, in the general setting, is that the asymptotic density of the sampling points is greater than the density of the corresponding weighted equilibrium measure of $M$, as defined in pluripotential theory. This result thus generalizes the well-known Landau type results for sampling on the torus, where the corresponding critical density corresponds to the Nyqvist rate, as well as the classical result saying that the zeros of orthogonal polynomials become equidistributed with respect to the logarithmic equilibrium measure, as the degree tends to infinity.-
dc.format.extent32 p.-
dc.publisherJohns Hopkins University Press-
dc.relation.isformatofReproducció del document publicat a:
dc.relation.ispartofAmerican Journal of Mathematics, 2018, vol. 140, num. 3, p. 789-820-
dc.rights(c) Johns Hopkins University Press, 2018-
dc.subject.classificationFuncions de diverses variables complexes-
dc.subject.classificationAnàlisi harmònica-
dc.subject.classificationAnàlisi de Fourier-
dc.subject.otherFunctions of several complex variables-
dc.subject.otherHarmonic analysis-
dc.subject.otherFourier analysis-
dc.titleSampling of real multivariate polynomials and pluripotential theory-
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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