Related papers: A footnote on Expanding maps
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where…
We consider analytic coupled map lattices over $\Z^d$ with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures with analytic, exponentially bounded finite dimensional…
We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not…
Given any smooth Anosov map we construct a Banach space on which the associated transfer operator is quasi-compact. The peculiarity of such a space is that in the case of expanding maps it reduces exactly to the usual space of functions of…
We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fr\'echet sequence spaces.…
The use of anisotropic Banach spaces has provided a wealth of new results in the study of hyperbolic dynamical systems in recent years, yet their application to specific systems is often technical and difficult to access. The purpose of…
We introduce a modified version of the Whitney extension operators for collections of functions from a closed subset of $\mathbb{R}^n$ into scales of Banach spaces with smoothing operators. We prove an extension theorem for collections…
It is well-known that, in Linear Dynamics, the most studied class of linear operators is certainly that of weighted shifts, on the separable Banach spaces $c_0$ and $\ell^p$, $1 \leq p< \infty$. Over the last decades, the intensive study of…
A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are H\"older spaces and Sobolev…
We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising from finite Blaschke products. This is achieved by deriving a convenient natural…
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…
Starting from the classic definitions of local resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and spectrum, the local space and the single-valued extention property of a…
We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the…
This paper is devoted to the study of strongly quasinonexpansive mappings in an abstract space and a Banach space.
We furnish a simple way of constructing an unbounded closed linear operator in a complex Banach space, whose spectrum is an arbitrary nonempty closed, in particular compact, subset of the complex plane.
We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted…
Two-dimensional maps with discontinuities are considered. It is shown that, in the presence of discontinuities, the essential spectrum of the transfer operator is large whenever it acts on a Banach space with norm that is stronger than…
We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure.…
In this paper we present complete description of the elements of Banach space with one-point spectrum. Some applications of these results are also given.
We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.