A representation theorem for certain partially ordered commutative rings

By T. Jacobi. 2001

84 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3ae25c26b4855aaed00fdcecf299a64bdc8fc514

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Citations in the corpus

Polynomials nonnegative on a grid and discrete optimization (2001, background): “For details and recent results, the interested reader is referred to Curto and Fialkow [2], Jacobi [3], Jacobi and Prestel [4, 5], Simon [12], Schmüdgen [11] and the many references therein.”
Global Optimization with Polynomials and the Problem of Moments (2000, background): “for some polynomials q(x), tk(x), k = 1, . . . , r, that are all sums of squares (see, e.g., Lemma 4.1 in Putinar [15] and also Jacobi [ 8 ]).”
Representations of Non-Negative Polynomials, Degree Bounds and Applications to Optimization (2009, background): “The quadratic module M is said to be archimedean if for each f ∈ A there exists an integer k ≥ 1 such that k − f ∈ M. Results of Putinar [14] and Jacobi [2] show that if R = R and the quadratic module M is archimedean, then for all f ∈ A, f > 0 on K ⇒ f ∈ M.”
Distinguished representations of non-negative polynomials (2005, background): “Let A be a Dedekind domain containing 12 , and assume that for every maximal ideal m of A the residue field A/m has at most one ordering.”
Bounds on measures satisfying moment conditions (2002, background): “, Putinar [13], Jacobi [8], Jacobi and Prestel [9]).”
Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas (2007, methodology): “One can use the spectral theorem as in [24], the Kadison-Dubois theorem as in [28] or Jabobi’s theorem [11].”
Optimization of Polynomial Functions (2003, methodology): “Jacobi gives another proof in [ 4 ] based on an extension of the Kadison-Dubois Theorem.”