Related papers: The Pressure Function for Products of Non-negative…

In this survey we discuss derivatives of the Wright functions (of the first and the second kind) with respect to parameters. Differentiation of these functions leads to infinite power series with coefficient being quotients of the digamma…

Clearly, a generalized inverse limit of metrizable spaces indexed by $\mathbb N$ is metrizable, as it is a subspace of a countable product of metrizable spaces. The authors previously showed that all idempotent, upper semi-continuous,…

We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to…

We develop the convex-analytic structure of the thermodynamic formalism for continuous maps on compact metric spaces. The pressure functional is the Legendre-Fenchel transform of the negative entropy, and the biconjugate recovery of the…

A weight function which $q$-generalizes the ground state wave function of the multi-component Calogero-Sutherland quantum many body system is introduced. Conjectures, and some proofs in special cases, are given for a constant term identity…

Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena…

This work introduces a new functional series for expanding an analytic function in terms of an arbitrary analytic function. It is generally applicable and straightforward to use. It is also suitable for approximating the behavior of a…

We give criteria on the existence of a so-called mark function in the context of marked metric measure spaces (mmm-spaces). If an mmm-space admits a mark function, we call it functionally-marked metric measure space (fmm-space). This is not…

The familiar cascade measures are sequences of random positive measures obtained on $[0,1]$ via $b$-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values.…

For real power series whose non-zero coefficients satisfy $|a_m|^{1/m}\to~1$ we prove a stronger version of Fabry theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.

Let $Z_n(s; a_1,..., a_n)$ be the Epstein zeta function defined as the meromorphic continuation of the function \sum_{k\in\Z^n\setminus\{0\}}(\sum_{i=1}^n [a_i k_i]^2)^{-s}, \text{Re} s>\frac{n}{2} to the complex plane. We show that for…

We consider stochastic dynamics of lattice systems with finite local state space, possibly at low temperature, and possibly non-reversible. We assume the additional regularity properties on the dynamics: a) There is at least one stationary…

Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…

Let $(X,d)$ be a compact metric space, and let an iterated function system (IFS) be given on $X$, i.e., a finite set of continuous maps $\sigma_{i}$: $ X\to X$, $i=0,1,..., N-1$. The maps $\sigma_{i}$ transform the measures $\mu $ on $X$…

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…

Starting from the full--shift on a finite alphabet $A$, mingling some symbols of $A$, we obtain a new full shift on a smaller alphabet $B$. This amalgamation defines a factor map from $(A^{\mathbb N},T_A)$ to $(B^{\mathbb N},T_B)$, where…

We develop a generalized control function approach to production function estimation. Our approach accommodates settings in which productivity evolves jointly with other unobservable factors such as latent demand shocks and the…

Working with well chosen Riemannian metrics and employing Nevanlinna's theory, we make the thermodynamical formalism work for a wide class of hyperbolic meromorphic functions of finite order (including in particular exponential family,…

We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum-free sets, $B_{h}[g]$-sets and Hilbert cubes. In…

If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms of the series. However, the partial sum approximation often…