Recursos de colección
Project Euclid (Hosted at Cornell University Library) (202.748 recursos)
Publicacions Matemàtique
Publicacions Matemàtique
Wang, Xiaoyuan; Chu, Wenchang
By means of the modified Abel lemma on summation by parts, we investigate infinite series involving quadratic and cubic harmonic numbers. Several infinite series identities are established for $\pi^2$ and $\zeta(3)$ as consequences.
Bergman, George M.
For $V$ a vector space over a field, or more generally, over a division ring, it is well-known that every $x\in\operatorname{End}(V)$ has an inner inverse; that is, that there exists $y\in\operatorname{End}(V)$ satisfying $xyx=x$. We show here that a large class of such $x$ have inner inverses $y$ that satisfy with $x$ an infinite family of additional monoid relations, making the monoid generated by $x$ and $y$ what is known as an inverse monoid (definition recalled). We obtain consequences of these relations, and related results. ¶ P. Nielsen and J. Šter [16] show that a much larger class of elements $x$...
Rutkowski, Artur
We present the theory of the Dirichlet problem for nonlocal operators which are the generators of general pure-jump symmetric Lévy processes whose Lévy measures need not be absolutely continuous. We establish basic facts about the Sobolev spaces for such operators, in particular we prove the existence and uniqueness of weak solutions. We present strong and weak variants of maximum principle, and $L^\infty$ bounds for solutions. We also discuss the related extension problem in $C^{1,1}$ domains.
Marcos, Miguel Andrés
The aim of this paper is to prove a trace theorem for Besov functions in the metric setting, generalizing a known result from A. Jonsson and H. Wallin in the Euclidean case. We show that the trace of a Besov space defined in a ‘big set’ $X$ is another Besov space defined in the ‘small set’ $F\subset X$. The proof is divided in three parts. First we see that Besov functions in $F$ are restrictions of functions of the same type (but greater regularity) in $X$, that is we prove an extension theorem and mention examples where this theorem holds....
Melián, María V.; Rodríguez, José M.; Tourís, Eva
In this paper we prove that for every complete $n$-dimensional Riemannian manifold without Green's function and with its sectional curvatures satisfying $K \le -1$, the exponent of convergence is greater than or equal to $n-1$. Furthermore, we show that this inequality is sharp. This result is well known for manifolds with constant sectional curvatures $K = -1$.
Azzam, Jonas
In a recent paper, Csörnyei and Wilson prove that curves in Euclidean space of $\sigma$-finite length have tangents on a set of positive $\mathscr{H}^{1}$-measure. They also show that a higher dimensional analogue of this result is not possible without some additional assumptions. In this note, we show that if $\Sigma\subseteq \mathbb{R}^{d+1}$ has the property that each ball centered on $\Sigma$ contains two large balls in different components of $\Sigma^{c}$ and $\Sigma$ has $\sigma$-finite $\mathscr{H}^{d}$-measure, then it has $d$-dimensional tangent points in a set of positive $\mathscr{H}^{d}$-measure. As an application, we show that if the dimension of harmonic measure for an...
Hagelstein, Paul; Parissis, Ioannis
Let $\mathsf M_{\mathsf{S}}$ denote the strong maximal operator on $\mathbb{R}^n$ and let $w$ be a non-negative, locally integrable function. For $\alpha\in(0,1)$ we define the weighted Tauberian constant $\mathsf C_{\mathsf {S},w}$ associated with $\mathsf M_{\mathsf{S}}$ by \[ \mathsf C_{\mathsf{S},w}(\alpha) := \sup_{\begin{subarray}{c} E\subset \mathbb{R}^n \\ 0\lt w(E) \lt+\infty\end{subarray}}\frac{1}{w(E)}w(\{x\in\mathbb{R}^n: \mathsf M_{\mathsf{S}}( {\mathbf 1}_E)(x)>\alpha\}). \] We show that $\lim_{\alpha\to 1^-} \mathsf C_{\mathsf {S},w}(\alpha)=1$ if and only if $w\in A_\infty^*$, that is if and only if $w$ is a strong Muckenhoupt weight. This is quantified by the estimate $\mathsf C_{\mathsf {S},w}(\alpha)-1\lesssim_{n} (1-\alpha)^{ (cn [w]_{A_\infty^*})^{-1}}$ as $\alpha\to 1^-$, where $c>0$ is a numerical constant independent of...
Buzzi, Claudio A.; Carvalho, Tiago; Euzébio, Rodrigo D.
In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. A Poincaré-Bendixson Theorem for a class of nonsmooth systems is presented. In addition, a minimal set in planar Filippov systems not predicted in classical Poincaré-Bendixson theory and whose interior is non-empty is exhibited. The concepts of limit sets, recurrence, and minimal sets for nonsmooth systems are defined and compared with the classical ones. Moreover some differences between them are pointed out.
da Silva, Jonatan F.; de Lima, Henrique F.; Velásquez, Marco Antonio L.
Given a positive function $F$ defined on the unit Euclidean sphere and satisfying a suitable convexity condition, we consider, for hypersurfaces $M^n$ immersed in the Euclidean space $\mathbb R^{n+1}$, the so-called $k$-th anisotropic mean curvatures $H_k^F$, $0\leq k\leq n$. For fixed $0\leq r\leq s\leq n$, a hypersurface $M^n$ of $\mathbb{R}^{n+1}$ is said to be $(r,s,F)$-linear Weingarten when its $k$-th anisotropic mean curvatures $H_k^F$, $r\leq k\leq s$, are linearly related. In this setting, we establish the concept of stability concerning closed $(r,s,F)$-linear Weingarten hypersurfaces immersed in $\mathbb R^{n+1}$ and, afterwards, we prove that such a hypersurface is stable if, and only...
Osȩkowski, Adam
For an integrable function $f$ on $[0,1)^d$, let $S(f)$ and $Mf$ denote the corresponding dyadic square function and the dyadic maximal function of $f$, respectively. The paper contains the proofs of the following statements. ¶ (i) If $w$ is a dyadic $A_1$ weight on $[0,1)^d$, then $$ ||S(f)||_{L^1(w)}\leq \sqrt{5}[w]_{A_1}^{1/2}||Mf||_{L^1(w)}. $$ The exponent $1/2$ is shown to be the best possible. ¶ (ii) For any $p>1$, there are no constants $c_p$, $\alpha_p$ depending only on $p$ such that for all dyadic $A_p$ weights $w$ on $[0,1)^d$, $$ ||S(f)||_{L^1(w)}\leq c_p[w]_{A_p}^{\alpha_p}||Mf||_{L^1(w)}. $$
Błaszczyk, Zbigniew; Kaluba, Marek
We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant, Dranishnikov, and Lubawski-Marzantowicz. In particular, it is bounded from above by Farber's topological complexity.
Kosz, Dariusz
In this article we characterize all possible cases that may occur in the rela- tions between the sets of $p$ for which weak type $(p; p)$ and strong type $(p; p)$ inequalities for the Hardy-Littlewood maximal operators, both centered and non-centered, hold in the context of general metric measure spaces.
Piersanti, Paolo; Pucci, Patrizia
Existence theorems of nonnegative entire solutions of stationary critical $p$-fractional Hardy Schrödinger Kirchhoff equations are presented in this paper. The equations we treat deal with Hardy terms and critical nonlinearities and the main theorems extend several recent results on the topic. The paper contains also some open problems.