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Title of Journal: Math Z

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Abbravation: Mathematische Zeitschrift

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Springer-Verlag

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10.1007/bf02320553

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1432-1823

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Positive semidefinite diagonal minus tail forms ar

Authors: Carla Fidalgo Alexander Kovacec
Publish Date: 2010/07/10
Volume: 269, Issue: 3-4, Pages: 629-645
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Abstract

By a diagonal minus tail form of even degree we understand a real homogeneous polynomial Fx 1 x n = Fx = Dx − Tx where the diagonal part Dx is a sum of terms of the form b i x i2d with all b i ≥ 0 and the tail Tx a sum of terms a i 1i 2cdots i nx 1i 1cdots x ni n with a i 1i 2cdots i n 0 and at least two i ν ≥ 1 We show that an arbitrary change of the signs of the tail terms of a positive semidefinite diagonal minus tail form will result in a sum of squares of polynomials We also give an easily tested sufficient condition for a polynomial to be a sum of squares of polynomials sos and show that the class of polynomials passing this test is wider than the class passing Lasserre’s recent conditions Another sufficient condition for a polynomial to be sos like Lasserre’s piecewise linear in its coefficients is also given

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Other Papers In This Journal:
  1. On profinite groups in which commutators are covered by finitely many subgroups
  2. Stable reduction of curves and tame ramification
  3. Constant mean curvature graphs on exterior domains of the hyperbolic plane
  4. On weighted critical imbeddings of Sobolev spaces
  5. Mixed Hessian inequalities and uniqueness in the class $$\mathcal {E}(X,\omega ,m)$$
  6. Generalized Liouville differentiation, truncated hypersingular integrals and K -functionals
  7. Polynomial inequalities and universal Taylor series
  8. Computations of the orbifold Yamabe invariant
  9. Grušin operators, Riesz transforms and nilpotent Lie groups
  10. Real K 3 surfaces without real points, equivariant determinant of the Laplacian, and the Borcherds Φ-function
  11. On the measures of large entropy on a positive closed current
  12. Fano varieties in index one Fano complete intersections
  13. Families over special base manifolds and a conjecture of Campana
  14. On the holomorphic structure of G -orbits in compact hermitian symmetric spaces
  15. Derivations, the Lawrence–Sullivan interval and the Fiorenza–Manetti mapping cone
  16. On the geometry of model almost complex manifolds with boundary
  17. The eta invariant in the doubly Kählerian conformally compact Einstein case
  18. Injectivity radius and diameter of the manifolds of flags in the projective planes
  19. On the invariant distributions of $$C^2$$ circle diffeomorphisms of irrational rotation number
  20. On Hörmander’s solution of the $$\bar{\partial }$$-equation. I
  21. Capillary surfaces in a convex cone
  22. Harmonic maps of finite uniton number into G 2
  23. On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms
  24. On irregular binomial D -modules
  25. Self-similar solutions for the Schrödinger map equation
  26. Harmonicity of sections of sphere bundles
  27. Cluster categories of type $${\mathbb {A}}_\infty ^\infty $$ and triangulations of the infinite strip
  28. A lower bound on Seshadri constants of hyperplane bundles on threefolds
  29. Saturated fusion systems over $$\mathcal {A}_2$$-groups
  30. Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature
  31. On newforms for Kohnen plus spaces
  32. Cumulants in noncommutative probability theory I. Noncommutative exchangeability systems
  33. Finiteness of the basic intersection cohomology of a Killing foliation
  34. Distributional chaos for operators with full scrambled sets
  35. Packing dimension and Ahlfors regularity of porous sets in metric spaces
  36. Invariance de la Γ-dimension pour certaines familles kählériennes de dimension 3
  37. Effective formulas for the local Łojasiewicz exponent
  38. Stein structures and holomorphic mappings
  39. Actions of arithmetic groups on homology spheres and acyclic homology manifolds
  40. Divergence form operators in Reifenberg flat domains
  41. Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups
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