Related papers: Piecewise Analytic Subactions for Analytic Dynamic…

In a seminal paper, Choquet introduced an integral formula to extend a monotone increasing setfunction on a sigma-algebra to a (nonlinear) functional on bounded measurable functions. The most important special case is when the setfunction…

In this paper we extend our previous results on the connectivity functions and pressure of the Random Cluster Model in the highly subcritical phase and in the highly supercritical phase, originally proved only on the cubic lattice $\Z^d$,…

In static analysis by abstract interpretation, one often uses widening operators in order to enforce convergence within finite time to an inductive invariant. Certain widening operators, including the classical one over finite polyhedra,…

Let $\Omega$ be a perfectly normal topological space, let $A$ be a non-empty $G_\delta$-subset of $\Omega$ and let $B_1(A)$ denote the space of all functions $A\to\mathbb{R}$ of Baire-one class on $A$. Let also $\|\cdot\|_\infty$ be the…

We show that alpha stable L\'evy motions can be simulated by any ergodic and aperiodic probability preserving transformation. Namely we show: - for $0<\alpha<1$ and every $\alpha$ stable L\'evy motion $\mathbb{W}$, there exists a function f…

If $f$ is a transcendental entire function with only algebraic singularities we calculate the Ruelle operator of $f$. Moreover, we prove both (i) if $f$ has a summable critical point, then $f$ is not structurally stable under certain…

Suppose $\sigma$ is the shift acting on Bernoulli space $X=\{0,1\}^\mathbb{N}$, and, consider a fixed function $f:X \to \mathbb{R}$, under the Waters's conditions (defined in a paper in ETDS 2007). For each real value $t\geq 0$ we consider…

For an analytic function f(z)=z+\sum_{n=2}^\infty a_n z^n satisfying the inequality \sum_{n=2}^\infty n(n-1)|a_n|\leq \beta, sharp bound on $\beta$ is determined so that $f$ is either starlike or convex of order $\alpha$. Several other…

This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…

For a function g(w) analytic and univalent in {w:1<|w|<\infty} with a simple pole at \infty and a continuous extension to {w:|w|\geq 1}, we consider the Faber polynomials F_n(z), n=0,1,2,..., associated to g(w) via their generating function…

We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant g_B for which we possess a finite number L of expansion coefficients plus two more informations: The…

We investigate the regularity of the positive roots of a non-negative function of one-variable. A modified H\"older space $\mathcal{F}^\beta$ is introduced such that if $f\in \mathcal{F}^\beta$ then $f^\alpha \in C^{\alpha \beta}$. This…

For analytic operator functions, we prove accumulation of branches of complex eigenvalues to the essential spectrum. Moreover, we show minimality and completeness of the corresponding system of eigenvectors and associated vectors. These…

We show that a function is real analytic at the origin iff it is arc-analytic, has a subanalytic graph, and its restriction to every monomial curve is analytic. This complements recent results of Kucharz and Kurdyka.

Let the sets of functions $Z$ and $\Omega$ be given on the time interval $T$, let there also be a multifunction (m/f) $\alpha$ acting from $\Omega$ to $Z$ and a finite set of moments $\Delta$ from $T$. The work deals with two questions: the…

Ruelle's transfer operator plays an important role in understanding thermodynamic and probabilistic properties of dynamical systems. In this work, we develop a method of finding eigenfunctions of transfer operators based on comparing Gibbs…

We introduce and study the class ${\bf\mathcal{G}}(\alpha,\beta)$ comprising analytic functions associated with a sector domain, where $\alpha,\beta\in(0,1]$. Using the extended version of Jack's lemma, we deduce Open-Door lemma type…

Let $f:X\to X$ be a continuous map on a compact metric space with finite topological entropy. Further, we assume that the entropy map $\mu\mapsto h_\mu(f)$ is upper semi-continuous. It is well-known that this implies the continuity of the…

We will consider a family of cellular automata $\Phi: \{1,2,...,r\}^\mathbb{N}\circlearrowright$ that are not of algebraic type. Our first goal is to determine conditions that result in the identification of probabilities that are at the…

Let $U$ be a bounded open subset of the complex plane and let $A_{\alpha}(U)$ denote the set of functions analytic on $U$ that also belong to the little Lipschitz class with Lipschitz exponent $\alpha$. It is shown that if $A_{\alpha}(U)$…