Sufficient conditions are established in order that, for a fixed infinite set of sampling points on the full line, a function satisfies a sampling theorem on a suitable closed subspace of a unitarily translation invariant reproducing kernel Hilbert space. A number of examples of such reproducing kernel Hilbert spaces and the corresponding sampling expansions are given. Sampling theorems for fun...

We study complex-valued symmetric matrices. A simple expression for the spectral norm of such matrices is obtained, by utilizing a unitarily congruent invariant form. Consequently, we provide a sharp criterion for identifying those symmetric matrices whose spectral norm does not exceed one: such strongly stable matrices are usually sought in connection with convergent difference approximations ...

An attractive candidate for the geometric mean of m positive definite matrices A1, . . . , Am is their Riemannian barycentre G. One of its important properties, monotonicity in the m arguments, has been established recently by J. Lawson and Y. Lim. We give a much simpler proof of this result, and prove some other inequalities. One of these says that, for every unitarily invariant norm, |||G||| ...

Let δa be a nontrivial dilation. We show that every complete norm ‖ · ‖ on L1(RN ) that makes δa from (L1(RN ), ‖ · ‖) into itself continuous is equivalent to ‖ · ‖1. δa also determines the norm of both C0(R ) and Lp(RN ) with 1 < p < ∞ in a weaker sense. Furthermore, we show that even all the dilations do not determine the norm on L∞(RN ).

In the context of Krylov methods for solving systems of linear equations, expressions and bounds are derived for the norm of the minimal residual, like the one produced by GMRES or MINRES. It is shown that the minimal residual norm is large as long as the Krylov basis is well-conditioned. In the context of non-normal matrices, examples are given where the minimal residual norm is a function of ...

We study multiplicative statistics for the eigenvalues of unitarily-invariant Hermitian random matrix models. consider one-cut regular polynomial potentials and a large class statistics. show that in limit several associated quantities converge to limits which are universal both potential family considered. In turn, such described by integro-differential Painlev\'e II equation, particular they ...

In this note, we consider the feedback connection of a plant M with a random matrix gain , and study the statistical properties of the loop gain L = M , under the hypothesis that the random feedback has a unitarily invariant distribution. This setup has interesting connections with two open problems related to the entropy of the plant, and to a probabilistic version of the multivariate Nyquist ...

We present a generally covariant and parity-invariant two-frame field ("zwei-dreibein") action for gravity in three space-time dimensions that propagates two massive spin-2 modes, unitarily, and we use Hamiltonian methods to confirm the absence of unphysical degrees of freedom. We show how zwei-dreibein gravity unifies previous "3D massive gravity" models and extends them, in the context of the...

An interesting result proved by Halmos in Hal (Michigan Mathematical Journal, 15, 215–223 (1968) is that the set of irreducible operators dense $${\mathcal {B}}({\mathcal {H}})$$ sense Hilbert-Schmidt approximation. In a von Neumann algebra {M}}$$ with separable predual, an operator $$a\in {\mathcal said to be if $$W^*(a)$$ subfactor , i.e., $$W^*(a)'\cap {M}}={{\mathbb {C}}} \cdot I$$ . Let $$...