Dynamics of Linear Operators: Author index

By Fr'ed'eric Bayart, É. Matheron. 2009

738 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f1e0cfede80f9f4bec84123c230c677dd19d0866

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Linear subsets of nonlinear sets in topological vector spaces (2013, background): “Excellent surveys for the theory of hypercyclicity and universality are [52], [97], [173], [174], [176], and [202].”
Frequently recurrent operators (2020, methodology): “.7 we obtain new proofs of Ansari-type and Leo´n-Mu¨ller type theorems for upper frequent hypercyclicity and frequent hypercyclicity that are due to Shkarin [42] and Bayart, Grivaux and Matheron [3], [5], respectively. The corresponding results for reiterative hypercyclicity follow with Theorem 2.1.”
m‐isometries on Banach spaces (2011, background): “For a complete account on hypercyclic operators, we refer to [5].”
Distributional chaos for linear operators (2013, background): “The study of the dynamics of linear operators on infinite-dimensional spaces has attracted attention of many researchers in recent years (we refer the reader to the books [4] and [11] for more information about this subject).”
Linear chaos and frequent hypercyclicity (2014, background): “4] and can be found in many papers [8, 11, 17, 20, 23, 25].”
A new class of frequently hypercyclic operators (2010, background): “We refer the reader to the recent book [6] for more information on these topics.”
Li–Yorke and distributionally chaotic operators (2010, background): “b(T,x) := {x,Tx,T2x,...} under a (continuous and linear) operator T : X → X on a topological vector space (usually, Banach or Fre´chet space) X, is dense in X. We refer the reader to the recent books [2] and [16] for a thorough account of the subject. This notion from operator theory joined chaos af”
Mixing operators and small subsets of the circle (2011, methodology): “[9]) and hence there is a very natural explicit ergodic Gaussian measure for Bw, namely the distribution of the random variable ξ = ∑∞ 0 gn w0···wn en.”
Lineability criteria, with applications (2013, background): “Recall that an operator T : X → X is said to be hypercyclic whenever it admits a dense orbit, that is, whenever there is a vector x0 ∈ X (called hypercyclic for T ) such that the set {T x0 : n ∈ N} is dense in X (see [15] and [60] for excellent surveys on this subject).”
Invariant measures for frequently hypercyclic operators (2014, background): “[4]), and since any proper Borel subspace ofX is Gauss null, i.”
Disjoint mixing operators (2012, methodology): “For general background on linear dynamics and hypercyclicity, we refer the reader to the recent books by Bayart and Matheron [3] and by Grosse-Erdmann and Peris Manguillot [20].”
Linear dynamical systems on Hilbert spaces: typical properties and explicit examples (2017, background): “Properties of unimodular eigenvectors of an operator T ∈ B(H) are closely related to those of invariant Gaussian measures for T (see for instance [5], [6], [8]): indeed, it turns out that in fact SPAN(H) = G-INVf (H) and PSPAN(H) = G-ERG(H); so that there was in fact no need for introducing new nota”