We provide an explicit description of the convex hull of the set of matrices of bounded rank, restricted to balls for the spectral norm. As applications, we deduce two relaxed forms of the rank function restricted to balls for the spectral norm: one is the quasiconvex hull of this rank function, another one is the convex hull of the rank function, thus retrieving Fazel's theorem (2002). Key-wor...

We show that solving the frequency assignment problem is equivalent to solving a minimization problem involving spectral norms of matrices, if the link gain matrix is symmetric. Often the spectral norm is ideal for minimization problems, but not so in this case. We reformulate the minimization using the one-, innnity-and Frobenius norm. This allows us to deal with non symmetric link gain matric...

We show that solving the frequency assignment problem is equivalent to solving a minimization problem involving spectral norms of matrices, if the link gain matrix is symmetric. Often the spectral norm is ideal for minimization problems, but not so in this case. We reformulate the minimization using the one-, innnity-and Frobenius norm. This allows us to deal with non symmetric link gain matric...

In this paper, we introduce the concept of interval pseudo-homegeneous uninorms. We extend the concept of pseudo-homogeneity of specific functions for interval pseudo-homogeneous functions. It is studied two cases of interval pseudo-homogeneous uninorms, that is, interval pseudo-homogeneous tnorms and interval pseudo-homogeneous t-conorms. It is proved a form of interval pseudo-homogeneous t-no...

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

Emmanuel Preissmann, Olivier Lévêque Swiss Federal Institute of Technology Lausanne, Switzerland Abstract In this paper, we study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, determinant, as well as various relations between the eigenvalues and eigenvectors of such matrices. We also study the asymptotic behaviour of the ...

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...