First, this paper provides characterizing the existence and uniqueness of linear operator solution T for large classes full Markov moment problems on closed subsets F Rn. One uses approximation by special nonnegative polynomials. The case when is compact studied. Then cases F=Rn F=R+n are under attention. Here, main findings consist in proving applying density polynomials, which sums squares, p...

We consider generators of algebraic covariant derivative curvature tensors R which can be constructed by a Young symmetrization of product tensors W ⊗ U or U ⊗ W , where W and U are covariant tensors of order 2 and 3. W is a symmetric or alternating tensor whereas U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2 1). Using Computer Alge...

Matrix extension with symmetry is to find a unitary square matrix P of 2π-periodic trigonometric polynomials with symmetry such that the first row of P is a given row vector p of 2πperiodic trigonometric polynomials with symmetry satisfying pp = 1. Matrix extension plays a fundamental role in many areas such electronic engineering, system sciences, wavelet analysis, and applied mathematics. In ...

We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomials.