Maximal and linearly inextensible polynomials
نویسندگان
چکیده
منابع مشابه
Maximal and Linearly Inextensible Polynomials
Let S(n, 0) be the set of monic complex polynomials of degree n ≥ 2 having all their zeros in the closed unit disk and vanishing at 0. For p ∈ S(n, 0) denote by |p|0 the distance from the origin to the zero set of p. We determine all 0-maximal polynomials of degree n, that is, all polynomials p ∈ S(n, 0) such that |p|0 ≥ |q|0 for any q ∈ S(n, 0). Using a second order variational method we then ...
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We consider the set S(n, 0) of monic complex polynomials of degree n ≥ 2 having all their zeros in the closed unit disk and vanishing at 0. For p ∈ S(n, 0) we let |p|0 denote the distance from the origin to the zero set of p. We determine all 0-maximal polynomials of degree n, that is, all polynomials p ∈ S(n, 0) such that |p|0 ≥ |q|0 for any q ∈ S(n, 0). Using a second order variational method...
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A quasi-polynomial is a function defined of the form q(k) = cd(k) k d + cd−1(k) k d−1 + · · · + c0(k), where c0, c1, . . . , cd are periodic functions in k ∈ Z. Prominent examples of quasipolynomials appear in Ehrhart’s theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the cj(k) for Ehrhart quasi-polynomials. For generic polyto...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2006
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-14999