Estimating L ∞ Norms by L 2k Norms for Functions on Orbits |
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Authors: | Barvinok |
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Institution: | (1) Department of Mathematics University of Michigan Ann Arbor, MI 48109-1109, USA barvinok@math.lsa.umich.edu, US |
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Abstract: | Abstract. Let G be a compact group acting in a real vector space V . We obtain a number of inequalities relating the L
∞ norm of a matrix element of the representation of G with its L
2k
norm for a positive integer k . As an application, we obtain approximation algorithms to find the maximum absolute value of a given multivariate polynomial
over the unit sphere (in which case G is the orthogonal group) and for the assignment problem of degree d , a hard problem of combinatorial optimization generalizing the quadratic assignment problem (in which case G is the symmetric group). |
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Keywords: | , Group representations, Matrix elements, Multivariate polynomials, Combinatorial optimization, Assignment problem,,,,,,Polynomial equations, Lp Norms, AMS Classification, 68W25, 68R05, 90C30, 90C27, 20C15, |
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