Abstract. For 2-variable weighted shifts W(α,β) ≡ (T1, T2) we study the invariance of (joint) khyponormality under the action (h, `) 7→ W (h,`) (α,β) := (T h 1 , T ` 2 ) (h, ` ≥ 1). We show that for every k ≥ 1 there exists W(α,β) such that W (h,`) (α,β) is k-hyponormal (all h ≥ 2, ` ≥ 1) but W(α,β) is not k-hyponormal. On the positive side, for a class of 2-variable weighted shifts with tensor...

In the present paper, we introduce the sequence space [{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {E_n}} x_j - sum_{j in E_{n + 1}} x_jright| ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of fin...

An analytical solution of the matrix Riemann-Hilbert problem relevant to the BGK modelin the field of rarefied-gas dynamics is used to deduce the partial indices basic to a canonicalsolution of the considered Riemann-Hilbert problem. SommarioSi fa uso di una soluzione analitica del problema di Riemann-Hilbert che origina dalmodello BGK nel campo della dinamica dei gas rarefa...

In this paper we unify the two subjects of implicitization and parametrization of nonsingular cubic surfaces. Beginning with a cubic parametrization with six basepoints, we first form a three by four Hilbert–Burch matrix, and then a three by three matrix of linear forms whose determinant is the implicit equation. Beginning with an implicit equation, we show how to construct a three by three mat...

A new, numerical framework for the approximation of solutions to matrix-valued Riemann–Hilbert problems is developed, based on a recent method for the homogeneous Painlevé II Riemann–Hilbert problem. We demonstrate its effectiveness by computing solutions to other Painlevé transcendents. An implementation in Mathematica is made available online.

The present paper is concerned with the existence2 of the eigenvalue ir of the Hilbert matrix A =((i+k —1)_1) or A = ((i+k)'1), i, k = l, 2, 3, • • • . It is well known that,3 considered as a linear operator in the Hilbert space I2 of vectors with finite square sum of components, A is symmetric, positive-definite and bounded, the upper bound being equal to ir. It is further known that4 ir is no...