The multiplicative Hilbert matrix

On additive and multiplicative Hilbert cubes

Given subset E of natural numbers FS(E) is defined as the collection of all sums of elements of finite subsets of E and any translation of FS(E) is said to be Hilbert cube.We can define the multiplicative analog of Hilbert cube as well. E.G. Strauss proved that for every ε > 0 there exists a sequence with density > 1− ε which does not contain an infinite Hilbert cube. In the present note we giv...

On the Hilbert Matrix, Ii1

where the best possible constant Mk is it for k ^ 1/2 and ir\ csc irk\ for 1/2 <k. Thus, when considered as a linear operator on the complex sequential Hilbert space l2, Hk is a bounded symmetric operator. Magnus [8] showed that the l2 spectrum of H0 is purely continuous and consists of the interval [0, it]. In this note we shall exhibit for each real k a monotone function pk(\) and an isometri...

Freeness of Multiplicative Matrix Semigroups

V. D. Blondel Department of Mathematical Engineering University of Louvain Avenue Georges Lemaitre, 4 B-1348 Louvain-la-Neuve Belgium Email: [email protected] J. Cassaigne Institut de Mathématiques de Luminy UPR 9016 Campus de Luminy, Case 907 13288 Marseille Cedex 9 France Email: [email protected] J. Karhumäki Dept. of Math. & TUCS University of Turku FIN-20014 Turku Finland Email: ...

Multiplicative diagonals of matrix semigroups

Computational Problems Concerning the Hilbert Matrix

Th e interaction b etwee n t heoretical mathematics and practical computational expire-m en t is illustrated by a discussion of recent work, at v arious centers, concerning t he Hilber t matrix.