On the spectrum of stochastic perturbations of the shift and Julia sets

el Houcein el Abdalaoui; Ali Messaoudi

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Displaying similar documents to “On the spectrum of stochastic perturbations of the shift and Julia sets”

Spectrum of L

W. Marek, K. Rasmussen

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CONTENTS0. Motivation, results to be used in the sequel ................51. Slicing $L_{α}$ ’s ..........................................................102. Hereditarily countable, definable elements ................133. Spectrum of L.............................................................154. The width of elements of spectrum ............................195. Non-uniform strong definability ..................................266. Solution to a problem of Wilmers................................327....

Fermi Golden Rule, Feshbach Method and embedded point spectrum

Jan Dereziński (1998-1999)

Séminaire Équations aux dérivées partielles

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A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jak $\overset{ˇ}{s}$ ić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.

Conditions equivalent to C* independence

Shuilin Jin, Li Xu, Qinghua Jiang, Li Li (2012)

Studia Mathematica

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Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , $S p (A, B) = S p (A) \times S p (B)$ , where Sp denotes the joint Taylor spectrum.

Ascent spectrum and essential ascent spectrum

O. Bel Hadj Fredj, M. Burgos, M. Oudghiri (2008)

Studia Mathematica

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We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if $σ_{a s c}^{e} (T + F) = σ_{a s c}^{e} (T)$ for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued...

Limit theorems for stochastic recursions with Markov dependent coefficients

Dariusz Buraczewski, Małgorzata Letachowicz (2012)

Colloquium Mathematicae

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We consider the stochastic recursion $X ₙ = A ₙ X_{n - 1} + B ₙ$ for Markov dependent coefficients (Aₙ,Bₙ) ∈ ℝ⁺ × ℝ. We prove the central limit theorem, the local limit theorem and the renewal theorem for the partial sums Sₙ = X₁+ ⋯ + Xₙ.

Extending the Wong-Zakai theorem to reversible Markov processes

Richard F. Bass, B. Hambly, Terry Lyons (2002)

Journal of the European Mathematical Society

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We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in $p$ -variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical...

Viability theorems for stochastic inclusions

Michał Kisielewicz (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Sufficient conditions for the existence of solutions to stochastic inclusions $x_{t} - x_{s} \in \int_{s}^{t} F_{τ} (x_{τ}) d τ + \int_{s}^{t} G_{τ} (x_{τ}) d w_{τ} + \int_{s}^{t} \int_{I R ⁿ} H_{τ, z} (x_{τ}) ν ̃ (d τ, d z)$ beloning to a given set K of n-dimensional cádlág processes are given.

Generalized spectral perturbation and the boundary spectrum

Sonja Mouton (2021)

Czechoslovak Mathematical Journal

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By considering arbitrary mappings $ω$ from a Banach algebra $A$ into the set of all nonempty, compact subsets of the complex plane such that for all $a \in A$ , the set $ω (a)$ lies between the boundary and connected hull of the exponential spectrum of $a$ , we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.

The norm spectrum in certain classes of commutative Banach algebras

H. S. Mustafayev (2011)

Colloquium Mathematicae

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Let A be a commutative Banach algebra and let $Σ_{A}$ be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by $σ (f) = \bar{f \cdot a : a \in A} \cap Σ_{A}$ , where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.

On the norm-closure of the class of hypercyclic operators

Christoph Schmoeger (1997)

Annales Polonici Mathematici

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Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if $f (σ_{W} (T)) \cup z \in ℂ : | z | = 1$ is connected, where $σ_{W} (T)$ denotes the Weyl spectrum of T.

Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity

Marc Peigné, Wolfgang Woess (2011)

Colloquium Mathematicae

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Consider a proper metric space and a sequence ${(F ₙ)}_{n \geq 0}$ of i.i.d. random continuous mappings → . It induces the stochastic dynamical system (SDS) $X ₙ^{x} = F ₙ \circ . . . \circ F ₁ (x)$ starting at x ∈ . In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the present first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying...

Spectra of extended double cover graphs

Zhibo Chen (2004)

Czechoslovak Mathematical Journal

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The construction of the extended double cover was introduced by N. Alon [1] in 1986. For a simple graph $G$ with vertex set $V = {v_{1}, v_{2}, \dots, v_{n}}$ , the extended double cover of $G$ , denoted $G^{*}$ , is the bipartite graph with bipartition $(X, Y)$ where $X = {x_{1}, x_{2}, \dots, x_{n}}$ and $Y = {y_{1}, y_{2}, \dots, y_{n}}$ , in which $x_{i}$ and $y_{j}$ are adjacent iff $i = j$ or $v_{i}$ and $v_{j}$ are adjacent in $G$ . In this paper we obtain formulas for the characteristic polynomial and the spectrum of $G^{*}$ in terms of the corresponding information of $G$ . Three formulas are derived for the number of spanning trees...

The principal spectrum for linear nonautonomous parabolic PDEs of second order: Space-independent case

Janusz Mierczyński (2001)

Colloquium Mathematicae

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We show that the study of the principal spectrum of a linear nonautonomous parabolic PDE of second order $u_{t} = Δ u + a (t) u$ on a bounded domain, with the Dirichlet or Neumann boundary conditions, reduces to the investigation of the spectrum of the linear nonautonomous ODE v̇ = a(t)v.

On the defect spectrum of an extension of a Banach space operator

Vladimír Kordula (1998)

Czechoslovak Mathematical Journal

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Let $T$ be an operator acting on a Banach space $X$ . We show that between extensions of $T$ to some Banach space $Y \supset X$ which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.

Some Results on Stochastic Porous Media Equations

Viorel Barbu, Giuseppe Da Prato, Michael Röckner (2008)

Bollettino dell'Unione Matematica Italiana

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Some recent results about nonnegative solutions of stochastic porous media equations in bounded open subsets of $\mathbb{R}^{3}$ are considered. The existence of an invariant measure is proved.