Related papers: On the exponential integrability of conjugate func…
We provide a general construction of integral TQFTs over a general commutative ring, $\mathbf{k}$, starting from a finite Hopf algebra over $\mathbf{k}$ which is Frobenius and double balanced. These TQFTs specialize to the Hennings…
Quasiregular mappings $f:\Omega\subset\R^{n}\to \R^{n}$ are a natural generalization of analytic functions from complex analysis and provide a theory which is rich with new phenomena. In this paper we extend a well-known result of A.~Chang…
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…
A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.
We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient…
The problem of computing the class expansion of some symmetric functions evaluated in Jucys-Murphy elements appears in different contexts, for instance in the computation of matrix integrals. Recently, M. Lassalle gave a unified algebraic…
We prove norm estimates for multilinear fractional integrals acting on weighted and variable Hardy spaces. In the weighted case we develop ideas we used for multilinear singular integrals [7]. For the variable exponent case, a key element…
It is shown in this paper that there is a fine correlation of the fourth order between the functions $Z^2[\vp_1(t)]$ and $\tilde{Z}^2(t)$, respectively. This correlation is with respect to two collections of disconnected sets. Corresponding…
We impose standard $ T1 $-type assumptions on a Calder\'on-Zygmund operator $ T $, and deduce that for bounded compactly supported functions $ f, g $ there is a sparse bilinear form $ \Lambda $ so that $$ \lvert \langle T f, g \rangle\rvert…
A set function can be extended to the unit cube in various ways; the correlation gap measures the ratio between two natural extensions. This quantity has been identified as the performance guarantee in a range of approximation algorithms…
Let $G/K$ be an orbit of the adjoint representation of a compact connected Lie group $G$, $\sigma$ be an involutive automorphism of $G$ and $\tilde G$ be the Lie group of fixed points of $\sigma$. We find a sufficient condition for the…
In this article we give a result obtained of an experimental way for the Euler totient function.
We extend the results of T. Giordano, I. F. Putnam, C. F. Skau contained in ``$\mathbb Z^d$-odometers and cohomology", Groups Geom. Dyn. 13 (2019), no. 3, P. 909-938, on characterization of conjugacy, isomorphism, and continuous orbit…
Using Cauchy's Integral Theorem as a basis, what may be a new series representation for Dirichlet's function $\eta(s)$, and hence Riemann's function $\zeta(s)$, is obtained in terms of the Exponential Integral function $E_{s}(i\kappa)$ of…
We extend the Kahane-Katznelson-de Leeuw theorem to smoothness spaces by showing that for any $g \in W^{l,2}(\mathbb{T}^d)$, there exists a function $f\in C^l(\mathbb{T}^d)$ satisfying $|\widehat{f}(n)|\geq |\widehat{g}(n)|$ and…
We prove an abstract result on the correlations of pairs of elements in an exponentially growing discrete subset $\mathcal E$ of $[0,+\infty[\,$ endowed with a weight function. Assume that there exist $\alpha\in\mathbb R$, $c,\delta>0$ such…
In this work we present a class of functions, motivated by gap functions, which we call G-coupling functions. We will show that these functions can generate a duality scheme for minimization problems by means of the general conjugation…
In this paper, we will study harmonic functions on the complete and incomplete spaces with nonnegative Ricci curvature which exhibit inhomogeneous collapsing behaviors at infinity. The main result states that any nonconstant harmonic…
This article establishes a real-variable argument for Zygmund's theorem on almost everywhere convergence of strong arithmetic means of partial sums of Fourier series on $\mathbb{T}$, up to passing to a subsequence. Our approach extends to,…
For any given Wulff shape $\mathcal{W}$, we can define the unique continuous function $S^{n}\to \mathbb{R}_{+}$ called convex integrand, denoted by $\gamma_{{}_{\mathcal{W}}}$. In this paper, we show that, for any Wulff shapes…