Loopy, Hankel, and combinatorially skew-Hankel tournaments

Loopy, Hankel, and combinatorially skew-Hankel tournaments

We investigate tournaments with a specified score vector having additional structure: loopy tournaments in which loops are allowed, Hankel tournaments which are tournaments symmetric about the Hankel diagonal (the anti-diagonal), and combinatorially skew-Hankel tournaments which are skew-symmetric about the Hankel diagonal. In each case, we obtain necessary and sufficient conditions for existen...

Finite rank intermediate Hankel operators and the big Hankel operator

Let La be a Bergman space. We are interested in an intermediate Hankel operator H M φ from La to a closed subspace M of L 2 which is invariant under the multiplication by the coordinate function z. It is well known that there do not exist any nonzero finite rank big Hankel operators, but we are studying same types in case H φ is close to big Hankel operator. As a result, we give a necessary and...

Stable factorization for Hankel and Hankel-like matrices

Multilinear Hankel Operator

We extend to multilinear Hankel operators a result on the regularity of truncations of Hankel operators. We prove and use a continuity property on the bilinear Hilbert transforms on product of Lipschitz spaces and Hardy spaces. In this note, we want to extend to multilinear Hankel operators a result obtained by [BB] on the boundedness properties of truncation acting on bounded Hankel infinite m...

Hankel hyperdeterminants and Selberg integrals

Abstract. We investigate the simplest class of hyperdeterminants defined by Cayley in the case of Hankel hypermatrices (tensors of the form Ai1i2...ik = f(i1+i2+· · ·+ik)). It is found that many classical properties of Hankel determinants can be generalized, and a connection with Selberg type integrals is established. In particular, Selberg’s original formula amounts to the evaluation of all Ha...