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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.
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.
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...
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...
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...
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...
q-Bernstein polynomials associated with q-stirling numbers and Carlitz's q-Bernoulli numbers
q-Bernstein polynomial Bernoulli numbers and polynomials
2010/12/8
Recently, T. Kim([4]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips([12]). In this paper, we give p-adic q-integral representation for Kim’s q-Bernstein po...
On p-adic analogue of q-Bernstein polynomials and related integrals
q-Bernstein polynomial Bernoulli numbers and poly-nomials p-adic q-integral
2010/12/8
Recently, T. Kim([5]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips q-Bernstein polynomials([11, 12]). The purpose of this paper is to study some propertie...
Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set
Higher-order recurrences Nikishin systems ratio asymptotics nth root asymptotics
2010/11/29
For a system of two measures supported on a starlike set in the complex plane, we study asymptotic properties of associated multiple orthogonal polynomials Qn and their recurrence coefficients. These ...
Some identities of Bernoulli numbers and polynomials associated with Bernstein polynomials
Bernstein polynomials Bosonic p-adic integrals
2010/11/26
We investigate some interesting properties of the Bernstein poly-nomials related to the bosonic p-adic integrals on Zp.
A note on q-Bernstein polynomials
q-Bernstein polynomials q-Euler numbers q-Stirling numbers
2010/11/26
Recently, Simsek-Acikgoz([17]) and Kim-Jang-Yi([9]) have studied the q-extension of Bernstein polynomials. In this paper we propose the q-extension of Bern-stein polynomials of degree n, which are dif...
Dvoretzky type theorems for multivariate polynomials and sections of convex bodies
Ramsey type theorems Dvoretsky’s theorem John’s ellipsoid.
2010/11/29
In this paper we prove the Gromov–Milman conjecture (the Dvoretzky typ theorem) for homogeneous polynomials on Rn, and improve bounds on the number n(d, k)in the analogous conjecture for odd degrees d...
Congruences on the Bell polynomials and the derangement polynomials
Bell polynomials Derangement polynomials Stirling numbers Congruences
2010/12/7
In this note, by the umbra calculus method, the Sun and Zagier’s congruences involving the Bell numbers and the derangement numbers are generalized to the polynomial cases. Some special congruences ar...
Orthogonality Relations for Multivariate Krawtchouk Polynomials
Multivariate orthogonal polynomial Hypergeometric function
2010/12/1
The orthogonality relations of multivariate Krawtchouk polynomials are discussed. For two variables case, an necessary and sufficient condition of orthogonality are given by Rahman and Gr¨unbaum in [1...