Institute for Systems Research

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

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Now showing 1 - 6 of 6
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    On the Converse to Pompeiu's Problem
    (1997) Berenstein, Carlos A.; ISR
    This is a reprint of a 1976 paper that appears in an inaccessible Brazilian journal and has become very looked after. It deals with the problem of determining a convex plane domain from the existence of infinitely many over determined Neumann eigenvalues. Recent related work in magneto hydrodynamics of Vogelius and other applications are closely related to this result. The more general result appears in J. Analyse Math 1980 and Crelle l987. See Zalcmain's bibliographic survey of pompeiu problem for other references.
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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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    Approximation by Spherical Waves in Lp-Space
    (1996) Agranovsky, Mark; Berenstein, Carlos A.; Kuchment, Peter; ISR
    We prove that functions of the form f(1x-a1), a in a closed surface, are dense in the space of all functions in Lp, for zn/(n+1). This property fails for 1zn/(n+1). By letting f be a Gsussian, we obtain a result about approximation by wavelets generated by the Gaussian.
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    Green Currents and Analytic Continuation
    (1995) Berenstein, Carlos A.; Yger, A.; ISR
    Using the construction of residue currents via analytic continuation we give explicit formulas for green currents which have singularities along algebraic varieties in projective space, as long as they are complete intersections.
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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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    Integral Geometry in Hyperbolic Spaces and Electrical Impedance Tomography
    (1994) Berenstein, Carlos A.; Tarabusi, E. Casadio; ISR
    We study the relation between convolution operators and the totally geodesic Radon transform on hyperbolic spaces. as an application we show that the linearized inverse conductivity problem in the disk can be interpreted exactly in terms of the X- ray transform with respect to the Poincare metric and of a simple convolution operator.