caa a22 4500 445836636 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0753-y doi (NATIONALLICENCE)springer-10.1007/s00209-010-0753-y Positive semidefinite diagonal minus tail forms are sums of squares [Elektronische Daten] [Carla Fidalgo, Alexander Kovacec] By a diagonal minus tail form (of even degree) we understand a real homogeneous polynomial F(x 1, . . . , x n ) = F(x) = D(x) − T(x), where the diagonal part D(x) is a sum of terms of the form $${b_i x_i^{2d}}$$ with all b i ≥ 0 and the tail T(x) a sum of terms $${a_{i_1i_2\cdots i_n}x_1^{i_1}\cdots x_n^{i_n}}$$ with $${a_{i_1i_2\cdots i_n} > 0}$$ 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. Springer-Verlag, 2010 Fidalgo Carla Dep. de Física e Matemática, Instituto Superior de Engenharia de Coimbra, 3030-199, Coimbra, Portugal aut Kovacec Alexander Dep. de Matemática, Universidade de Coimbra, 3001-454, Coimbra, Portugal aut Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 629-645 0025-5874 269:3-4<629 2011 269 209 https://doi.org/10.1007/s00209-010-0753-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0753-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fidalgo Carla Dep. de Física e Matemática, Instituto Superior de Engenharia de Coimbra, 3030-199, Coimbra, Portugal aut NATIONALLICENCE 700 1- Kovacec Alexander Dep. de Matemática, Universidade de Coimbra, 3001-454, Coimbra, Portugal aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 629-645 0025-5874 269:3-4<629 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer