Related papers: The Basic Reproduction Number for Bounded Linear O…
We introduce a numerical radius operator space $(X, \mathcal{W}_n)$. The conditions to be a numerical radius operator space are weaker than the Ruan's axiom for an operator space $(X, \mathcal{O}_n)$. Let $w(\cdot)$ be the numerical radius…
We consider the SIRWJS epidemiological model that includes the waning and boosting of immunity via secondary infections. We carry out combined analytical and numerical investigations of the dynamics. The formulae describing the existence…
The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also…
This paper is devoted to the study of the asymptotic behavior of the principal eigenvalue and basic reproduction ratio associated with periodic population models in a patchy environment for small and large dispersal rates. We first deal…
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space…
It is shown that an elliptic scattering operator $A$ on a compact manifold with boundary with coefficients in the bounded operators of a bundle of Banach spaces of class (HT) and Pisier's property $(\alpha)$ has maximal regularity (up to a…
The goal of this paper is to study band-dominated operators on Banach spaces with Schauder basis with respect to uniformly locally finite metric spaces as well as the Banach algebras generated by them: the so called uniform Roe algebras. We…
A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The…
Well-bounded operators are linear operators on a Banach space $X$ that have an $AC[a,b]$ functional calculus for some interval $[a,b]$. A well-bounded operator is of type (B) if it can be written as an integral against a spectral family of…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking, where rational speed invasion fronts…
We establish criteria for the stability of the essential spectrum for unbounded operators acting in Banach modules. The applications cover operators acting on sections of vector fiber bundles over non-smooth manifolds or locally compact…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
We study linear operators $T$ on Banach spaces for which there exists a $C_0$-semigroup $(T(t))_{t\geq 0}$ such that $T=T(1)$. We present a necessary condition in terms of the spectral value 0 and give classes of examples where this can or…
We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-order Radon probability measure on such a space is uniquely…
We consider, through PDE methods, branching Brownian motion with drift and absorption. It is well know that there exists a critical drift which separates those processes which die out almost surely and those which survive with positive…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
The Restricted Isometry Property (RIP) is a fundamental property of a matrix enabling sparse recovery. Informally, an m x n matrix satisfies RIP of order k in the l_p norm if ||Ax||_p \approx ||x||_p for any vector x that is k-sparse, i.e.,…
Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.