Results 31 to 40 of about 106 (90)
Dynamics, Operator Theory, and Infinite Holomorphy
, 2014 Abstract and Applied Analysis, Volume 2014, Issue 1, 2014.
Alfred Peris +3 more
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Genericity of wild holomorphic functions and common hypercyclic vectors
Advances in Mathematics, 2004 If \(X\) is a Fréchet space and \(T :X\to X\) is a continuous linear operator, then \(T\) is called hypercyclic if there is a vector \(x\in X\) whose orbit \(\{x,Tx,T^2x,\dots\}\) is dense in \(X\). In this case, \(x\) is called a hypercyclic vector for \(T\).
Costakis, George, Sambarino, Martı́n
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Common hypercyclic vectors and universal functions
, 2015 Let X,Y be two separable Banach or Frechet spaces , and (Tn) , n=1,2,... be a sequence from linear and continuous operators from X to Y . We say that the sequence (Tn) , n=1,2,... is universal , if there exists some vector v in X such that the sequence Tn(v) , n=1,2,... is dense in Y . If X=Y we say that the sequence (Tn) is hypercyclic .More generally
Costakis, George, Tsirivas, Nikos
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Existence of Hypercyclic Operators on Topological Vector Spaces
Journal of Functional Analysis, 1997 The author establishes the following result: Suppose \(X\) is a topological vector space with a bounded biorthogonal system \(\{x_n, f_n\}\). Suppose \(X\) is \(\ell^1\)-complete with respect to \((x_n)\). (a) If \(\widetilde T: X\to X\) is continuous and \(\widetilde T(x_n)= w_nx_{n-1}\) for some bounded sequence \((w_n)\) of positive real numbers ...
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Hypercyclic vectors and algebras
, 2021 Ce travail contribue à la théorie de l'hypercyclicité et à des concepts liés. Nous nous sommes principalement intéressés à des algèbres de vecteurs hypercycliques pour opérateurs agissant sur une algèbre de Fréchet de suites, bien que quelques contributions portent sur l'existence d'un seul vecteur.
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On chaotic 𝐶₀-semigroups and infinitely regular hypercyclic vectors [PDF]
Proceedings of the American Mathematical Society, 2006 A C 0 C_0 -semigroup
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A hypercyclicity criterion for non-metrizable topological vector spaces [PDF]
Functiones et Approximatio Commentarii Mathematici, 2018 We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition operator on the space of real analytic functions on $]0,1[$, which solves two problems of Bonet and Domański \cite ...
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Frequently Hypercyclic Random Vectors
, 2023 Some results concerning the existence of almost surely frequently hypercyclic random vectors have been proved in the literature for certain chaotic weighted shifts. This is of interest for at least two reasons. It is usually difficult to find explicit (frequently) hypercyclic vectors, and random vectors have a probability distribution whose ergodic ...
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Common hypercyclic vectors for families of backward shift operators [PDF]
Journal of Operator Theory, 2017 We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the full orbit of the backward shift.
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Discrete cyclic systems and circle congruences. [PDF]
Ann Mat Pura Appl, 2022 Hertrich-Jeromin U, Szewieczek G.
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