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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.
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.
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...
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...
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...
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...
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...
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...
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 ...
We investigate some interesting properties of the Bernstein poly-nomials related to the bosonic p-adic integrals on Zp.
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...
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...
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...
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...

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