Results 21 to 30 of about 752 (101)
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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On the set of hypercyclic vectors for the differentiation operator [PDF]
Israel Journal of Mathematics, 2010 Let $D$ be the differentiation operator $Df=f'$ acting on the Fr chet space $\H$ of all entire functions in one variable with the standard (compact-open) topology. It is known since 1950's that the set $H(D)$ of hypercyclic vectors for the operator $D$ is non-empty.
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Frequently hypercyclic random vectors
Proceedings of the American Mathematical Society, 2022 We show that, under suitable conditions, an operator acting like a shift on some sequence space has a frequently hypercyclic random vector whose distribution is strongly mixing for the operator. This result will be applied to chaotic weighted shifts.
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Invariant Manifolds of Hypercyclic Vectors [PDF]
Proceedings of the American Mathematical Society, 1993 We show that any hypercyclic operator on Hilbert space has a dense, invariant linear manifold consisting, except for zero, entirely of hypercyclic vectors.
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Hypercyclic algebras for D-multiples of convolution operators [PDF]
, 2018 It is shown in this short note the existence, for each nonzero member of the ideal of D-multiples of convolution operators acting on the space of entire functions, of a scalar multiple of it supporting a hypercyclic algebra.Plan Andaluz de Investigación (
Bernal González, Luis +1 more
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Algebrable sets of hypercyclic vectors for convolution operators [PDF]
Israel Journal of Mathematics, 2020 We show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff's operator also has this property on the space of complex-valued smooth functions on the real line.
Bès, Juan, Papathanasiou, Dimitris
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Monsters in Hardy and Bergman spaces [PDF]
, 2002 A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary.
Bernal González, Luis +1 more
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Difference sets and frequently hypercyclic weighted shifts [PDF]
, 2013 We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on $\ell^p(\mathbb Z)$, $p\geq 1$.
Bayart, Frédéric, Ruzsa, Imre
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Abstract and Applied Analysis, Volume 2018, Issue 1, 2018., 2018 The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear) multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
G. M. N’Guérékata +2 more
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S‐Mixing Tuple of Operators on Banach Spaces
Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016 We consider the question: what is the appropriate formulation of Godefroy‐Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators, S‐mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to be S‐mixing.
Wei Wang +3 more
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