Institute for Systems Research

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Author: search.filters.author.Berenstein, Carlos A.Subject: search.filters.subject.system theory

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Now showing 1 - 3 of 3
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    Residue Calculus and Effective Nullstellensatz
    (1996) Berenstein, Carlos A.; Yger, A.; ISR
    We provide new tools to compute multidimensional residues for rational functions, even over fields of positive characteristic. As a corollary one obtains solutions of the Betout equation for polynomials over a ring with a site that have almost optimal estimates for degree and size.
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    Resudus, Courants residuels et Courants de Green
    (1994) Berenstein, Carlos A.; Gay, Roger; Yger, A.; ISR
    Some explicit formulas are provided in order to solve division problems in commutative algebra or questions related to intersection theory; it is shown here how the ides of analytic continuation of distributions leads to some explicit solution for Green equation for algebraic complete intersections in the projective space.
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    Interpolating Varieties for Spaces of Meromorphic Functions
    (1992) Berenstein, Carlos A.; Li, Bao Q.; ISR
    Various interesting results on interpolation theory of entire functions with given growth conditions have been obtained by imposing conditions on multiplicity varieties and weights. All the results discussed in the literature are limited to the space of entire functions. In this paper, we shall extend and generalize the interpolation problem of entire functions to meromorphic functions. The analytic conditions sufficient and necessary for a given multiplicity variety to be interpolating for meromorphic functions with given growth conditions will be obtained. Moreover, purely geometric characterization of interpolating varieties will be given for slowly decreasing radial weights which enable us to determine whether or not a given multiplicity variety is an interpolating variety by direct calculation. when weights grow so rapidly as to allow infinite order functions in the considered space, the geometric conditions would become more delicate. For such weights p(z), we also find purely geometric sufficient as well as necessary conditions provided that log p(exp r) is convex. As corollaries of our results, one obtains the corresponding results for the interpolation of entire functions.