Explicit Constructions of Dense Common Hypercyclic Subspaces

Abstract We give an explicit construction of a dense infinite dimensional vector space of hypercyclic vectors for the weighted backward shift T λ (|λ| > 1). We also develop a technique to construct common hypercyclic vectors for countable families of these operators. The techniques developed here do not rely on the Baire category theorem or any kind of existence proof, as do most approaches to this problem. §1. Introduction and Preliminaries If X denotes an infinite dimensional separable Banach space and T : X → X is a bounded linear operator on X, we say that x ∈ X is a hypercyclic vector for T if its orbit, {T n x : n ∈ N}, is dense in X. If there exists such an x ∈ X we call T a hypercyclic operator. The problem of characterizing certain families of hypercyclic operators has been intensively studied in the last twenty years. A very famous family of such operators is the weighted backward shift. Given X an infinite dimensional Banach space, we will say that X admits a weighted backward shift, T λ , if X has a Schauder basis, (e i ) i , and the operator x n e n → n≥2 λ · x n e n−

Magnetic Pseudodifferential Operators

Abstract In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in R n under the influence of a variable magnetic field B. It incorporates phase factors defined by B and reproduces the usual Weyl calculus for B = 0. In the present article we develop the classical pseudodifferential theory of this formalism for the standard symbol classes S m ρ,δ . Among others, we obtain properties and asymptotic developments for the magnetic symbol multiplication, existence of parametrices, boundedness and positivity results, properties of the magnetic Sobolev spaces. In the case when the vector potential A has all the derivatives of order ≥ 1 bounded, we show that the resolvent and the fractional powers of an elliptic magnetic pseudodifferential operator are also pseudodifferential. As an application, we get a limiting absorption principle and detailed spectral results for self-adjoint operators of the form H = h(Q, Π A ), where h is an elliptic symbol, Q denotes multiplication with the variables Π A = D − A, D is the operator of derivation and A is the vector potential corresponding to a short-range magnetic field

Structural Crack Identification in Railway Prestressed Concrete Sleepers Using Dynamic Mode Shapes

Railway prestressed concrete sleepers are a structural and safety-critical component in railway tracks. [...

Enterprise Risk Management: Review, Critique, and Research Directions

Many regulators, rating agencies, executives and academics have advocated a new approach to risk management: Enterprise Risk Management (ERM). ERM proposes the integrated management of all the risks an organization faces, which inherently requires alignment of risk management with corporate governance and strategy. Academic research on ERM is still in its infancy, with articles largely in accounting and finance journals but rarely in management journals. We argue that ERM offers an important new research domain for management scholars. A critical review of ERM research allows us to identify limitations and gaps that management scholars are best equipped to address. This paper not only identifies how management scholars can contribute to ERM research, but also points out why ERM research (and practice) needs management research for its development. (C) Elsevier Ltd. All rights reserved