It is shown that an innnite Hankel matrix of a nite rank (or a nite Hankel matrix) admits a generalized Vandermonde decomposition H = V T DV , where V is a generalized Vandermonde matrix, and D is a block diagonal matrix. The full structure of this decomposition was rst fully discussed by Vandevoorde 9], but the development here is based solely on linear algebra considerations, speciically the ...

It is a well known fact that the generalized Vandermonde determinant can be expressed as the product of the standard Vandermonde determinant and a polynomial with nonnegative integer coefficients. In this paper we generalize this result to Vandermonde determinants over the Chebyshev basis. We apply this result to prove that the number of real roots in [1;1] of a real polynomial is bounded by th...

Abstract We review several determinant and Pfaffian identities, which generalize the evaluation formulae of Cauchy’s determinant det (1/(xi + yj)) and Schur’s Pfaffian Pf ((xj − xi)/(xj + xi)). As a multi-variable generalization, we consider Cauchytype determinants and Schur-type Pfaffians of matrices with entries involving some generalized Vandermonde determinants. Also we give an elliptic gen...

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Z...

We show here that the refined theorems for both lecture hall partitions and anti-lecture hall compositions can be obtained as straightforward consequences of two q-Chu Vandermonde identities, once an appropriate recurrence is derived. We use this approach to get new lecture hall-type theorems for truncated objects. The truncated lecture hall partitions are sequences (λ1, . . . , λk) such that λ...

In this paper we analyze completeness results for basic narrowing. We show that basic narrowing is not complete with respect to normalizable solutions for equational theories defined by confluent term rewriting systems, contrary to what has been conjectured. By imposing syntactic restrictions on the rewrite rules we recover completeness. We refute a result of Hölldobler which states the complet...

The purpose of this paper is to study the conditioning of complex Vandermonde matrices, in reference to applications such as superresolution and the problem of recovering missing samples in band-limited signals. The results include bounds for the singular values of Vandermonde matrices whose nodes are complex numbers on the unit circle. It is shown that, under certain conditions, such matrices ...