Related papers: On extending C^k functions from an open set to R, …

Let $ \mathbb{F}_q[T]$\, be the ring of polynomials over a finite field $ \mathbb{F}_q $. Let $ g: \mathbb{F}_q[T] \rightarrow \mathbb{R} $ be a multiplicative function such that for any irreducible polynomial $ P $ over $ \mathbb{F}_q $…

In the present work we carry on the study of the order theory for ($\mathcal{C}^{\infty}-$-reduced) $\mathcal{C}^{\infty}-$-rings initiated in \cite{rings1} (see also \cite{BM2}). In particular, we apply some results of the order theory of…

Using Dupire's notion of vertical derivative, we provide a functional (path-dependent) extension of the It\^o's formula of Gozzi and Russo (2006) that applies to C^{0,1}-functions of continuous weak Dirichlet processes. It is motivated and…

We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value $1$ at $(1,1,\ldots, 1)$. We characterize the existence of a $k$-increasing…

In classical complex analysis analyticity of a complex function $f$ is equivalent to differentiability of its real and imaginary parts $u$ and $v$, respectively, together with the Cauchy-Riemann equations for the partial derivatives of $u$…

Based on a well known Sh.-T. Yau theorem we obtain that the real part of a holomorphic function on a K\"{a}hler manifold with the Ricci curvature bounded from below by $-1$ is contractive with respect to the distance on the manifold and the…

Let (G,S) be a Coxeter group. We construct a continuation, to the open unit disc, of the unitary representations associated to the positive definite functions g -> r^l(g). (Here 0<r<1, and l denotes the length function with respect to the…

Let $\cal{P}$ be an open filter base for a filter $\cal{F}$ on $X$. We denote by $C^{\cal{P}}(X)$ ($C_{\infty\cal{P}}(X)$) the set of all functions $f\in C(X)$ where $Z(f)$ ($\{x: |f(x)|< \frac{1}{n}\})$ contains an element of $\cal{P}$.…

Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…

Inspired by the idea of blurring the exponential function, we define blurred variants of the $j$-function and its derivatives, where blurring is given by the action of a subgroup of $\rm{GL}_2(\mathbb{C})$. For a dense subgroup (in the…

In $\C^2=\R^2+i\R^2$ with coordinates $z=(z_1,z_2), z=x+iy$, we consider a function $f$ continuous on a domain $\Omega$ of $\R^2$ separately real analytic in $x_1$ and CR extendible to $y_2$ (resp. CR extendible to $y_2>0$). This means that…

Let X=H\G be a homogeneous spherical variety for a split reductive group G over the integers o of a p-adic field k, and K=G(o) a hyperspecial maximal compact subgroup of G=G(k). We compute eigenfunctions ("spherical functions") on X=X(k)…

For a rational function f we consider the norm of the derivative with respect to the spherical metric and denote by K(f) the supremum of this norm. We give estimates of this quantity K(f) both for an individual function and for sequences of…

Given a finite group $G$ acting on a ring $R$, Merling constructed an equivariant algebraic $K$-theory $G$-spectrum, and work of Malkiewich and Merling, as well as work of Barwick, provides an interpretation of this construction as a…

For any positive integer $k$, we prove the existence of nontrivial $C^k$-smooth uniformly rotating solutions to the 2D incompressible Euler equations with compact spatial support. These solutions, which can be chosen to be small…

Let $M$ be a complex manifold, $D\subset M$ a free divisor and $U=M\setminus D$ its complement. In this paper we study the characteristic cycle $\textup{CC}(\gamma\cdot \ind_U)$ of the restriction of a constructible function $\gamma$ on…

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass $\mathcal{P}_{\tau,\mu}(k,\delta,\gamma)$ of analytic and univalent functions in the open…

We study the units in a tensor product of rings. For example, let k be an algebraically closed field. Let A and B be reduced rings containing k, having connected spectra. Let u \in A tensor_k B be a unit. Then u = a tensor_k b for some…

We establish generic existence of Universal Taylor Series on products $\Omega = \prod \Omega_i$ of planar simply connected domains $\Omega_i$ where the universal approximation holds on products $K$ of planar compact sets with connected…

Let $C$ be a subset of $\mathbb{R}^n$ (not necessarily convex), $f:C\to\mathbb{R}$ be a function, and $G:C\to\mathbb{R}^n$ be a uniformly continuous function, with modulus of continuity $\omega$. We provide a necessary and sufficient…