Hypercyclicity and unimodular point spectrum

By Fr'ed'eric Bayart, S. Grivaux. 2005

61 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dab8646e37f08ebfeda073b27b34d43cc4918136

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Szemeredi's theorem, frequent hypercyclicity and multiple recurrence (2010, background): “A more recent notion relevant to hypercyclicity, which examines how often the orbit of a hypercyclic vector visits a non-empty open set, was introduced by Bayart and Grivaux in [2], [3]:”
Frequently hypercyclic operators and vectors (2007, background): “Now, Bayart and Grivaux call x frequently hypercyclic if it meets every such set U ‘often’ in the sense of positive lower density.”
Difference sets and frequently hypercyclic weighted shifts (2013, background): “By [1], there exists a dense set X0 ⊂ X such that T n x→ 0 for all x ∈ X0.”
Distributional chaos for linear operators (2013, background): “5 in [1]) and thus there exists a dense set X0 such that limn→∞ T x = 0 for all x ∈ X0.”
On a Theorem of Godefroy and Shapiro (2006, unknown): “Theorem 3.2 (Bayart and Grivaux [1], [ 2 ], [3]).”
A new class of frequently hypercyclic operators (2010, methodology): “In the works [3], [5], [17], invariant measures were constructed using sums of independent Gaussian variables ∑ gn(ω)xn, and taking advantage of the rotational invariance of the law of gn.”
Hilbertian Jamison sequences and rigid dynamical systems (2011, methodology): “Kalish constructed in [21] an example of a bounded operator on a Hilbert space whose point spectrum is equal to L, and, as in [3], we use this example for our purposes: let T0 be the operator defined on L2(T) by T0 = M−J , whereMf(λ) = λf(λ) and Jf(λ) = ∫ (1,λ) f(ζ)dζ for any f ∈ L2(T) and λ ∈ T.”
Recurrent Linear Operators (2013, background): “In fact, in this case, T is frequently hypercyclic; see [5,6,29,30].”
Unimodular eigenvalues, uniformly distributed sequences and linear dynamics (2007, background): “Operators with perfectly spanning set of eigenvectors associated to unimodular eigenvalues are always hypercyclic (see [3]) and when X is a Hilbert space, they are frequently hypercyclic (see [4], and [5] for a study of what happens in the general Banach space case).”