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Eric Weber

  1. Iterative approximations of exponential bases on fractal measures.

    Fri, 09/23/2011 - 15:01 — SomNambul
    Authors: Eric Weber, Dorin Ervin Dutkay, Deguang Han
    Subjects: Functional Analysis
    Abstract

    For some fractal measures it is a very difficult problem in general to prove
    the existence of spectrum (respectively, frame, Riesz and Bessel spectrum). In
    fact there are examples of extremely sparse sets that are not even Bessel
    spectra. In this paper we investigate this problem for general fractal measures
    induced by iterated function systems (IFS). We prove some existence results of
    spectra associated with Hadamard pairs.

  2. The moduli space of $1|2$-dimensional complex associative algebras.

    Mon, 11/02/2009 - 16:01 — SomNambul
    Authors: Michael Penkava, Chris DeCleene, Carolyn Otto, Mitch Phillipson, Ryan Steinbach, Eric Weber
    Subjects: Rings and Algebras
    Abstract

    In this paper, we study the moduli space of $1|2$-dimensional complex
    associative algebras, which is also the moduli space of codifferentials on the
    tensor coalgebra of a $2|1$-dimensional complex space. We construct the moduli
    space by considering extensions of lower dimensional algebras. We also
    construct miniversal deformations of these algebras. This gives a complete
    description of how the moduli space is glued together via jump deformations.

  3. Hearing the Hausdorff dimension.

    Thu, 10/29/2009 - 16:01 — SomNambul
    Authors: Eric Weber, Dorin Ervin Dutkay, Deguang Han, Qiyu Sun
    Subjects: Functional Analysis
    Abstract

    We study Fourier frames of exponentials on fractal measures. We prove that,
    for affine iterated function system measures, the Beurling dimension of a
    Fourier frame must coincide with the Hausdorff dimension of the fractal. We
    present necessary and/or sufficient conditions for a set of frequencies to form
    a Bessel sequence or a frame of exponential functions.

  4. The moduli space of $2|1$-dimensional complex associative algebras.

    Mon, 10/26/2009 - 14:11 — SomNambul
    Authors: Michael Penkava, Chris DeCleene, Carolyn Otto, Mitch Phillipson, Ryan Steinbach, Eric Weber
    Subjects: Rings and Algebras
    Abstract

    In this paper, we study the moduli space of $2|1$-dimensional complex
    associative algebras, which is also the moduli space of codifferentials on the
    tensor coalgebra of a $1|2$-dimensional complex space. We construct the moduli
    space by considering extensions of lower dimensional algebras. We also
    construct miniversal deformations of these algebras. This gives a complete
    description of how the moduli space is glued together via jump deformations.

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