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Fejer-Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle
Fejer-Riesz factorizations the structure of bivariate polynomials orthogonal the bi-circle Complex Variables
2012/6/29
We give a complete characterization of the positive trigonometric polynomials Q(\theta,\phi) on the bi-circle, which can be factored as Q(\theta,\phi)=|p(e^{i\theta},e^{i\phi})|^2 where p(z,w) is a po...
Some results on zeros distributions and uniqueness of derivatives of difference polynomials
Zeros difference polynomials derivatives value sharing uniqueness
2011/8/25
Abstract: We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conj...
Best $\ell_1$-approximation of nonnegative polynomials by sums of squares
Polynomials sums of squares semidefinite programming
2011/2/21
Given a nonnegative polynomial f, we provide an explicit expres-sion for its best ℓ1-norm approximation by a sum of squares of given degree.
Zeta functions and Bernstein-Sato polynomials for ideals in dimension two
Zeta functions Bernstein-Sato polynomials ideals dimension two
2011/2/28
For a nonzero ideal I ⊳C[x1, . . . , xn], with 0 ∈ supp I, a (general-ized) conjecture of Igusa–Denef–Loeser predicts that every pole of its topologi-cal zeta function is a root of its Bernstein...
Vector valued Jack polynomials associated to the symmetric group
SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik-Dunkl...
Maximal fillings of moon polyominoes, simplicial complexes, and Schubert polynomials
filling of moon polyomino k-triangulation fan of Dyck paths
2010/12/10
We exhibit a canonical connection between maximal (0, 1)-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation.
The idea of orthogonal polynomials is well established and has many appli-cations. For any commutative moments {Si}.
Polynomials non-negative on strips and half-strips
Polynomials non-negative strips half-strips
2010/12/8
Throughout, we work in the real polynomial ring in two variables, which we denote by R[x; y]. The set of sums of squares in R[x; y] is denoted by P R[x; y]2. Recently,M. Marshall [4] settled a long-st...
Primitive prime divisors in zero orbits of polynomials
Primitive prime divisors zero orbits of polynomials
2010/12/9
Let (bn) = (b1, b2, . . . ) be a sequence of integers. A primitive prime divisor of a term bk is a prime which divides bk but does not divide any of the previous terms of the sequence. A zero orbit of...
Betti numbers of toric varieties and eulerian polynomials
Betti numbers of toric varieties eulerian polynomials
2010/12/3
It is well-known that the Eulerian polynomials, which count permutations in Sn by their number of descents, give the h-polynomial/h-vector of the simple polytopes known as permutohedra, the convex hul...
Direct spreading measures of Laguerre polynomials
Orthogonal polynomials Laguerre polynomials spreading lengths
2010/11/26
The direct spreading measures of the Laguerre polynomials L( )n (x), which quantify the distribution of its Rakhmanov probability density n, (x) = 1 d2 n x e−x h L( ) n (x)
i2 along the positi...
Arguments of zeros of highly log concave polynomials
Arguments of zeros highly log concave polynomials
2010/12/14
For a real polynomial p =Pn i=0 cixi with no negative coefficients and n ≥ 6, let β(p) = infn−1 i=1 c2i /ci+1ci−1 (so β(p) ≥ 1 entails that p is log concave). If β(p) > 1.45 . . . , then a...
Minimal Polynomials of Some Matrices Via Quaternions
Minimal Polynomials Some Matrices Via Quaternions
2010/11/26
This work provides explicit characterizations and formulae for the minimal polynomials of
a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and
orthogonal matrices. A...
Asymptotics of orthogonal polynomials and point perturbation on the unit circle
point masses bounded variation asymptotics of orthog-onal polynomials Kooman’s theorem
2010/12/1
In the first five sections, we deal with the class of probability measures with asymptotically periodic Verblunsky co-efficients of p-type bounded variation. The goal is to investigate
the perturbati...
Every Banach ideal of polynomials is compatible with an operator ideal
Polynomial ideals operator ideals
2010/11/30
We show that for each Banach ideal of homogeneous polynomials, there exists a (necessarily unique) Banach operator ideal compatible with it. Analogously, we prove that any ideal of n-homogeneous polyn...