High-dimensional Menger-type curvatures. Part I: Geometric multipoles and multiscale inequalities
نویسندگان
چکیده
منابع مشابه
High-Dimensional Menger-Type Curvatures - Part I: Geometric Multipoles and Multiscale Inequalities
We define discrete Menger-type curvature of d+2 points in a real separable Hilbert space H by an appropriate scaling of the squared volume of the corresponding (d+1)-simplex. We then form a continuous curvature of an Ahlfors regular measure μ on H by integrating the discrete curvature according to products of μ (or its restriction to balls). The essence of this work, which continues in a subseq...
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This is the second of two papers wherein we estimate multiscale least squares approximations of certain measures by Menger-type curvatures (defined in Part I). More specifically, we study an arbitrary d-regular measure μ on a real separable Hilbert space, where d ∈ N. The main result of this paper bounds the least squares error of approximating μ at any ball B by an average of the discrete Meng...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2011
ISSN: 0213-2230
DOI: 10.4171/rmi/645