Related papers: Power substitution in quasianalytic Carleman class…

In this note, we present new properties for a sequence arising in some refinements of Carleman's inequality. Our results extend some results of Yang [Approximations for constant e and their applications J. Math. Anal. Appl. 262 (2001)…

We establish new sufficient conditions for the existence of classical hyperbolic quasiperiodic solutions for natural Lagrangian system on Riemannian manifold with time-quasiperiodic force function

The main purpose of this paper is to give characterization theorems on derivations as well as on linear functions. Among others the following problem will be investigated: Let $n\in\mathbb{Z}$, $f, g\colon\mathbb{R}\to\mathbb{R}$ be…

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by…

A remarkable theorem of Joris states that a function $f$ is $C^\infty$ if two relatively prime powers of $f$ are $C^\infty$. Recently, Thilliez showed that an analogous theorem holds in Denjoy--Carleman classes of Roumieu type. We prove…

We develop a convolution theory for quasianalytic ultradistributions of Gelfand-Shilov type. We also construct a special class of ultrapolynomials, and use it as a base for the parametrix method in the study of new topological and…

Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…

Symmetry plays a basic role in variational problems (settled e.g. in $\mathbb R^{n}$ or in a more general manifold), for example to deal with the lack of compactness which naturally appear when the problem is invariant under the action of a…

The classical Waring problem deals with expressing every natural number as a sum of g(k) kth powers. Similar problems for finite simple groups have been studied recently, and in this paper we study them for finite quasisimple groups G. We…

For a Gaussian process $X$ and smooth function $f$, we consider a Stratonovich integral of $f(X)$, defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on $X$ such that the sequence converges…

Let $\mathbb{G}$ be a higher-rank connected semisimple Lie group with finite center and without compact factors. In any unitary representation $(\pi, \mathcal{H})$ of $\mathbb{G}$ without non-trivial $\mathbb{G}$-fixed vectors, we study the…

Let $\mathcal C^M$ denote a Denjoy-Carleman class of $\mathcal C^\infty$ functions (for a given logarithmically-convex sequence $M = (M_n)$). We construct: (1) a function in $\mathcal C^M((-1,1))$ which is nowhere in any smaller class; (2)…

This expository article is devoted to the local theory of ultradifferentiable classes of functions, with a special emphasis on the quasianalytic case. Although quasianalytic classes are well-known in harmonic analysis since several decades,…

We show that the leading semiclassical behavior of soliton form factors at arbitrary momentum transfer is controlled by solutions to a new wave-like integro-differential equation that describes solitons undergoing acceleration. We work in…

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…

Let $(X,\omega)$ be a compact K\"ahler manifold of dimension $n$ and fix $m\in \mathbb{N}$ such that $1\leq m \leq n$. We prove that any $(\omega,m)$-sh function can be approximated from above by smooth $(\omega,m)$-sh functions. A…

In this article, we investigate the weighted $m-$subharmonic functions. We shall give some properties of this class and consider its relation to the $m-$Cegrell classes. We also prove an integration theorem and an almost everywhere…

The need to describe abrupt changes or response of nonlinear systems to impulsive stimuli is ubiquitous in applications. Also the informal use of infinitesimal and infinite quantities is still a method used to construct idealized but…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

We consider the class $\Sigma(p)$ of univalent meromorphic functions $f$ on $\ID$ having simple pole at $z=p\in[0,1)$ with residue 1. Let $\Sigma_k(p)$ be the class of functions in $\Sigma(p)$ which have $k$-quasiconformal extension to the…