Related papers: Exponential dichotomy and $(L^p,L^q)$-admissibilit…

Recently, G.~Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note is twofold: we extend Yanev's theorem by relaxing a…

We study linear control systems in infinite--dimensional Banach spaces governed by analytic semigroups. For $p\in[1,\infty]$ and $\alpha\in\RR$ we introduce the notion of $L^p$--admissibility of type $\alpha$ for unbounded observation and…

We give a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by product, we obtain a simple proof of an interesting…

The aim of this paper is to give necessary and sufficient conditions for the uniform exponential trichotomy property of nonlinear evolution operators in Banach spaces. The obtained results are generalizations for infinite-dimensional case…

For a nontrivial locally compact group $G$, and $p\in [1,\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. We show that these Banach algebras are…

Let $G$ be a locally compact group, and take $p\in(1,\infty)$. We prove that the Banach left $L^1(G)$-module $L^p(G)$ is injective (if and) only if the group $G$ is amenable. Our proof uses the notion of multi-norms. We also develop the…

We obtain an equivalent implicit characterization of $L^p$ Banach spaces that is amenable to a logical treatment. Using that, we obtain an axiomatization for such spaces into a higher-order logical system, the kind of which is used in proof…

In the paper, we introduce the concept of weight with reasonable growth on a locally compact group $G$. We verify that these weights form a natural class to work with, by examining the most common examples. We proceed with the discussion of…

If $X$ is an almost transitive Banach space with amenable isometry group (for example, if $X=L^p([0,1])$ with $1\leqslant p<\infty$) and $X$ admits a uniformly continuous map $X\overset\phi\longrightarrow E$ into a Banach space $E$…

We consider a finite number of orientation preserving $C^2$ interval diffeomorphisms and apply them randomly in such a way that the expected Lyapunov exponents at the boundary points are positive. We prove the exponential decay of…

We show weighted non-autonomous $L^q(L^p)$ maximal regularity for families of complex second-order systems in divergence form under a mixed regularity condition in space and time. To be more precise, we let $p,q \in (1,\infty)$ and we…

We shall first study summability of families in normed spaces indexed with well ordered sets of real numbers extended by infinity. Obtained results and a generalized iteration method are applied to derive necessary and sufficient conditions…

The {\lambda}-exponential family has recently been proposed to generalize the exponential family. While the exponential family is well-understood and widely used, this it not the case of the {\lambda}-exponential family. However, many…

In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability…

In this paper, ordinary and exponential dichotomies are defined in differential equations with equations with piecewise constant argument of general type. We prove the asymptotic equivalence between the bounded solutions of a linear system…

We introduce the notion of (strong) subexponential growth for \'etale groupoids and study its basic properties. In particular, we show that the K-groups of the associated groupoid $L^p$-operator algebras are independent of $p \in…

We consider a supercritical branching process $(Z_n)$ in a random environment $\xi$. Let $W$ be the limit of the normalized population size $W_n=Z_n/E[Z_n|\xi]$. We first show a necessary and sufficient condition for the quenched $L^p$…

Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences…

We prove the exponential law $\mathcal A(E \times F, G) \cong \mathcal A(E,\mathcal A(F,G))$ (bornological isomorphism) for the following classes $\mathcal A$ of test functions: $\mathcal B$ (globally bounded derivatives), $W^{\infty,p}$…

In this paper we aim to establish some results depending on the comparative growth properties of composite transcendental entire or meromorphic functions and some special type of differential polynomials generated by one of the factors on…