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rss_1.0 Recursos de colección

Project Euclid (Hosted at Cornell University Library) (171.728 recursos)

Publicacions Matemàtique

Mostrando recursos 1 - 20 de 151

1. A characterization of hyperbolic Kato surfaces - Brunella, Marco
We give a characterization of hyperbolic Kato surfaces in terms of the existence of an automorphic Green function on a cyclic covering. This is achieved by analysing a naturally defined Levi-flat foliation, and by perturbing certain Levi-flat leaves to strictly pseudoconvex hypersurfaces.

2. On rings with finite number of orbits - Hryniewicka, Małgorzata; Krempa, Jan
Let $R$ be an associative unital ring with the unit group $U(R)$. Let $\mathcal{S}$ denote one of the following sets: the set of elements of $R$, of left ideals of $R$, of principal left ideals of $R$, or of ideals of $R$. Then the group $U(R)\times U(R)$ acts on the set $\mathcal{S}$ by left and right multiplication. In this note we are going to discuss some properties of rings $R$ with a finite number of orbits under the action of $U(R)\times U(R)$ on $\mathcal{S}$.

3. (Weak) compactness of Hankel operators on \boldmath$\mathit{BMOA}$ - Papadimitrakis, Michael
We prove that the notions of compactness and weak compactness for a Hankel operator on $\mathit{BMOA}$ are identical.

4. Non-existence of multi-line Besicovitch sets - Orponen, Tuomas
If a compact set $K \subset \mathbb{R}^{2}$ contains a positive-dimensional family of line-segments in every direction, then $K$ has positive measure.

5. Generalized quasidisks and conformality - Guo, Chang-Yu; Koskela, Pekka; Takkinen, Juhani
We introduce a weaker variant of the concept of linear local connectivity, sufficient to guarantee the extendability of a conformal map $f\colon\mathbb D\to\Omega$ to the entire plane as a homeomorphism of locally exponentially integrable distortion. Additionally, we show that a conformal map as above cannot necessarily be extended in this manner if we assume that $\Omega$ is the image of $\mathbb D$ under a self-homeomorphism of the plane that has locally exponentially integrable distortion.

6. Submanifolds with nonparallel first normal bundle revisited - Dajczer, Marcos; Tojeiro, Ruy
In this paper, we analyze the geometric structure of a Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very special type. We also give a sharp estimate of the dimension of the rulings.

7. Dilations and full corners on fractional skew monoid rings - Pardo, E.
In this note we will show that the dilation result obtained for fractional skew monoid rings, in the case of a cancellative left Ore monoid $S$ acting on a unital ring $A$ by corner isomorphisms, holds in full generality. We apply this result to the context of semigroup $C^*$-crossed products.

8. Weak and viscosity solutions of the fractional Laplace equation - Servadei, Raffaella; Valdinoci, Enrico
Aim of this paper is to show that weak solutions of the following fractional Laplacian equation $$(-\Delta)^s u=f &\Omega\\u=g &\mathbb R^n\setminus\Omega$$ ¶ are also continuous solutions (up to the boundary) of this problem in the viscosity sense. ¶ Here $s\in(0,1)$ is a fixed parameter, $\Omega$ is a bounded, open subset of $\mathbb R^n$ ($n\geqslant1$) with $C^2$-boundary, and $(-\Delta)^s$ is the fractional Laplacian operator, that may be defined as $$(-\Delta)^su(x):=c(n,s)\int\limits_{\mathbb R^n}\frac{2u(x)-u(x+y)-u(x-y)}{|y|^{n+2s}}\,dy,$$ ¶ for a suitable positive normalizing constant $c(n,s)$, depending only on $n$ and $s$. ¶ In order to get our regularity result we first prove a maximum principle and then, using it, an interior and boundary regularity...

9. Convergence of Lagrange interpolation series in the Fock spaces - Dumont, André; Kellay, Karim
We study the uniqueness sets, the weak interpolation sets, and convergence of the Lagrange interpolation series in radial weighted Fock spaces.

10. Dynamics of (pseudo) automorphisms of 3-space: periodicity versus positive entropy - Bedford, Eric; Kim, Kyounghee
We study the iteration of the family of maps given by $3$-step linear fractional recurrences. This family was studied earlier from the point of view of finding periodicities. In this paper we finish that study by determining all possible periods within this family. The novelty of our approach is that we apply the methods of complex dynamical systems. This leads to two classes of interesting pseudo automorphisms of infinite order. One of the classes consists of completely integrable maps. The other class consists of maps of positive entropy which have an invariant family of $K3$ surfaces.

11. Revisiting the Fourier transform on the Heisenberg group - Lavanya, R. Lakshmi; Thangavelu, S.
A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on $ {\mathbb R}^{n} $ as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group

12. The oriented graph of multi-graftings in the Fuchsian case - Calsamiglia, Gabriel; Deroin, Bertrand; Francaviglia, Stefano
We prove the connectedness and compute the diameter of the oriented graph of multi-graftings associated to exotic $\mathbb{CP}^1$-structures on a compact surface~$S$ with a given holonomy representation of Fuchsian type.

13. Marcinkiewicz interpolation theorems for Orlicz and Lorentz gamma spaces - Kerman, Ron; Phipps, Colin; Pick, Lubosš
Fix the indices $\alpha$ and $\beta$, $1<\alpha<\beta<\infty$, and suppose $\varrho$ is an Orlicz gauge or Lorentz gamma norm on the real-valued functions on a set $X$ which are measurable with respect to a~$\sigma$-finite measure $\mu$ on it. Set $$M(\gamma,X):=\{f\colon X\to\mathbb R \text{ with } \sup_{\lambda>0}\lambda \mu(\{x\in X: |f(x)|>\lambda\})^{\frac1{\gamma}}<\infty\},$$ ¶ $\gamma=\alpha,\beta$. In this paper we obtain, as a special case, simple criteria to guarantee that a linear operator $T$ satisfies $T\colon L_{\varrho}(X)\to L_{\varrho}(X)$, whenever $T\colon M(\alpha,X)\to M(\alpha, X)$ and $T\colon M(\beta,X)\to M(\beta, X)$.

14. Vanishing results for the cohomology of complex toric hyperplane complements - Davis, M. W.; Settepanella, S.
Suppose $\mathcal R$ is the complement of an essential arrangement of toric hyperlanes in the complex torus $(\mathbb{C}^*)^n$ and $\pi=\pi_1(\mathcal R)$. We show that $H^*(\mathcal R;A)$ vanishes except in the top degree $n$ when $A$ is one of the following systems of local coefficients: (a) a system of nonresonant coefficients in a complex line bundle, (b) the von Neumann algebra $\mathcal{N}\pi$, or (c) the group ring ${\mathbb Z} \pi$. In case (a) the dimension of $H^n$ is $|e(\mathcal R)|$ where $e(\mathcal R)$ denotes the Euler characteristic, and in case (b) the $n^{\mathrm{th}}$ $\ell^2$ Betti number is also $|e(\mathcal R)|$

15. Entropy and Flatness in Local Algebraic Dynamic - Majidi-Zolbanin, Mahdi; Miasnikov, Nikita; Szpiro, Lucien
For a local endomorphism of a noetherian local ring we introduce a notion of entropy, along with two other asymptotic invariants. We use this notion of entropy to extend numerical conditions in Kunz' regularity criterion to every contracting endomorphism of a noetherian local ring, and to give a characteristic-free interpretation of the definition of Hilbert-Kunz multiplicity. We also show that every finite endomorphism of a complete noetherian local ring of equal characteristic can be lifted to a finite endomorphism of a complete regular local ring. The local ring of an algebraic or analytic variety at a point fixed by a finite self-morphism inherits a local endomorphism whose entropy is...

16. An Extension of Sub-Fractional Brownian Motion - Sghir, Aissa
In this paper, firstly, we introduce and study a self-similar Gaussian process with parameters $H \in{(0,1)}$ and $K \in(0,1]$ that is an extension of the well known sub-fractional Brownian motion introduced by Bojdecki et al. Secondly, by using a decomposition in law of this process, we prove the existence and the joint continuity of its local time

17. Conjugacy classes of left ideals of a finite dimensional algebra - Mȩcel, Arkadiusz; Okniński, Jan
Let $A$ be a finite dimensional unital algebra over a field $K$ and let $C(A)$ denote the set of conjugacy classes of left ideals in $A$. It is shown that $C(A)$ is finite if and only if the number of conjugacy classes of nilpotent left ideals in $A$ is finite. The set~$C(A)$ can be considered as a semigroup under the natural operation induced from the multiplication in $A$. If $K$ is algebraically closed, the square of the radical of~$A$ is zero and $C(A)$ is finite, then for every $K$-algebra $B$ such that $C(B)\cong C(A)$ it is shown that $B\cong A$.

18. Blei's Inequality and Coordinatewise Multiple Summing Operators - Popa, Dumitru; Sinnamon, Gord
Two inequalities resembling the multilinear Hölder inequality for mixed-norm Lebesgue spaces are proved. When specialized to single-function inequalities they include a pair of inequalities due to Blei and a recent extension of Blei's inequality. The first of these inequalities is applied to give explicit indices in a known result for coordinatewise multiple summing operators. The second is used to prove a complementary result to the known one, again with explicit indices. As an application of the complementary result, a sufficient condition is given for a composition of operators to be multiple summing.

19. Layer potentials beyond singular integral operator - Rosén, Andreas
We prove that the double layer potential operator and the gradient of the single layer potential operator are $L_2$ bounded for general second order divergence form systems. As compared to earlier results, our proof shows that the bounds for the layer potentials are independent of well posedness for the Dirichlet problem and of De Giorgi-Nash local estimates. The layer potential operators are shown to depend holomorphically on the coefficient matrix $A\in L_\infty$, showing uniqueness of the extension of the operators beyond singular integrals. More precisely, we use functional calculus of differential operators with non-smooth coefficients to represent the layer potential operators as bounded Hilbert space operators. In the presence...

20. Polygonal $\mathcal{VH}$ Complexes - Polák, Jason K. C.; Wise, Daniel T.
Ian Leary inquires whether a class of hyperbolic finitely presented groups are residually finite. We answer in the affirmative by giving a systematic version of a construction in his paper, which shows that the standard $2$-complexes of these presentations have a $\mathcal{VH}$-structure. This structure induces a splitting of these groups, which together with hyperbolicity, implies that these groups are residually finite.

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