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Common zeros preserving maps on vector-valued function spaces and Banach modules
http://ddd.uab.cat/record/160583
Let X, Y be Hausdorff topological spaces, and let E and F be Hausdorff topological vector spaces. For certain subspaces A (X,E) and A(Y, F) of C(X,E) and C(Y, F) respectively (including the spaces of Lipschitz functions), we characterize surjections S, T : A (X;E) → A(Y, F), not assumed to be linear, which jointly preserve common zeros in the sense that Z (f – f’) ∩ Z (f – f’) ∩ Z (g – g’) ≠ 0 if and only if Z (Sf – Sf’) ∩ Z (Tg – Tg´) ≠ 0 for all f, f’, g, g’ ∈ A (X, E). Here Z (·)denotes the zero set of a function. Using the notion of point multipliers we extend the notion of zero set for the elements of a Banach module and give a representation for surjective linear maps which jointly preserve common zeros in module case. Hosseini, MalihehThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605832016Convergence of functions of self-adjoint operators and applications
http://ddd.uab.cat/record/160582
The main result (roughly) is that if Hi converges weakly to H and if also f (Hi) converges weakly to f(H), for a single strictly convex continuous function f, then (Hi) must converge strongly to H. One application is that if f(pr(H)) = pr(f(H)), where pr denotes compression to a closed subspace M, then M must be invariant for H. A consequence of this is the verification of a conjecture of Arveson, that Theorem 9. 4 of [Arv] remains true in the infinite dimensional case. And there are two applications to operator algebras. If h and f(h) are both quasimultipliers, then h must be a multiplier. Also (still roughly stated), if h and f(h) are both in pAsap, for a closed projection p, then h must be strongly q-continuous on p. Brown, Lawrence G.Thu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605822016Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings
http://ddd.uab.cat/record/160581
We consider a family of dissipative active scalar equations outside the L2-space. This was introduced in [7] and its velocity fields are coupled with the active scalar via a class of multiplier operators which morally behave as derivatives of positive order. We prove global well-posedness and time-decay of solutions, with-out smallness assumptions, for initial data belonging to the critical Lebesgue space Ln/2y-β (ℝn ) which is a class larger than that of the above reference. Symmetry properties of solutions are investigated depending on the symmetry of initial data and coupling operators. Ferreira, Lucas C. F.Thu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605812016Röver's simple group is of type F ∞
http://ddd.uab.cat/record/160580
We prove that Claas Röver's Thompson-Grigorchuk simple group V G has type F∞. The proof involves constructing two complexes on which V G acts: a simplicial complex analogous to the Stein complex for V , and a polysimplicial complex analogous to the Farley complex for V . We then analyze the descending links of the polysimplicial complex, using a theorem of Belk and Forrest to prove increasing connectivity. Belk, JamesThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605802016Integral restriction for bilinear operators
http://ddd.uab.cat/record/160579
We consider the integral domain restriction operator TΩ for certain bilinear operator T. We obtain that if (s, p1, p2) satisfies 1 p1+ 1 p2 ≥ 2 min{1,s} and kTkLp1 ×Lp2→Ls < ∞, then kTΩkLp1 ×Lp2→Ls < ∞. For some special domain Ω, this property holds for triplets (s, p1, p2) satisfying 1 p1 + 1 p2 > 1 min{1,s}. Zhao, WeirenThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605792016The Kato Square Root Problem follows from an extrapolation property of the Laplacian
http://ddd.uab.cat/record/160578
On a domain Ω ⊆ _ Rd we consider second-order elliptic systems in divergence-form with bounded complex coefficients, realized via a sesquilinear form with domain H1/0 (Ω) ⊆ V ⊆ H1 (Ω). Under very mild assumptions on Ω and V we show that the solution to the Kato Square Root Problem for such systems can be deduced from a regularity result for the fractional powers of the negative Laplacian in the same geometric setting. This extends earlier results of McIntosh [25] and Axelsson-Keith-McIntosh [6] to non-smooth coefficients and domains. Egert, MoritzThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605782016A monotonicity formula for minimal sets with a sliding boundary condition
http://ddd.uab.cat/record/160577
We prove a monotonicity formula for minimal or almost minimal sets for the Hausdorff measure Hd, subject to a sliding boundary constraint where competitors for E are obtained by deforming E by a one-parameter family of functions yt such that yt(x) ∈ L when x ∈ E lies on the boundary L. In the simple case when L is an affine subspace of dimension d-1, the monotone or almost monotone functional is given by F(r) = r-d Hd (E∩B(x, r)) + r-d Hd (S∩B(x,r)) where x is any point of E (not necessarily on L) and S is the shade of L with a light at x. We then use this, the description of the case when F is constant, and a limiting argument, to give a rough description of E near L in two simple cases. David, GuyThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605772016Vitali's theorem without uniform boundedness
http://ddd.uab.cat/record/160576
Let {fm}m≥1 be a sequence of holomorphic functions defined on a bounded domain D ⊂ Cn or a sequence of rational functions (1 ≤ deg rm ≤ m) defined on Cn. We are interested infinding sufficient conditions to ensure the convergence of {fm}m≥1 on a large set provided the convergence holds pointwise on a not too small set. This type of result is inspired from a theorem of Vitali which gives a positive answer for uniformly bounded sequence. Quang Dieu, NguyenThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605762016Summation of coefficients of polynomials on Lp spaces
http://ddd.uab.cat/record/160575
We investigate the summability of the coefficients of m-homogeneous polynomials and m-linear mappings defined on `p spaces. In our research we obtain results on the summability of the coefficients of m-linear mappings defined on Lp1 x . . . x Lpm. The first results in this respect go back to Littlewood [17] and Bohnenblust and Hille [6] for bilinear and m-linear forms on c0, and Hardy and Littlewood [15] and Praciano-Pereira [20] for bilinear and m-linear forms on arbitrary `p spaces. Our results recover and in some case complete these old results through a general approach on vector valued m-linear mappings. Dimant, VerónicaThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605752016Entire spacelike -graphs in Lorentzian product spaces
http://ddd.uab.cat/record/160574
In this work we establish suffcient conditions to ensure that an entire spacelike graph immersed with constant mean curvature in a Lorentzian product space, whose Riemannian fiber has sectional curvature bounded from below, must be a trivial slice of the ambient space. Lima, Henrique F. deThu, 14 Jul 2016 06:36:05 GMThttp://ddd.uab.cat/record/1605742016Some local properties defining To-groups and related classes of groups
http://ddd.uab.cat/record/144969
We call G a HallX -group if there exists a normal nilpotent subgroup N of G for which G/N0 is an X-group. We call G a T0-group provided G/Φ(G) is a T -group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define HallX -groups and T0-groups where X ∈ {T , PT , PST }; the classes PT and PST denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations. 2010 Mathematics Subject Classification: Primary: 20D10, 20D20, 20D35. Ballester-Bolinches, A.Wed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449692016Extreme cycles :: the center of a Leavitt path algebra
http://ddd.uab.cat/record/144968
In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path algebra with the aim of giving a description of the center. Extreme cycles appear for the first time; they concentrate the purely infinite part of a Leavitt path algebra and, jointly with the line points and vertices in cycles without exits, are the key ingredients in order to determine the center of a Leavitt path algebra. Our work will rely on our previous approach to the center of a prime Leavitt path algebra [13]. We will go further into the structure itself of the Leavitt path algebra. For example, the ideal I(Pec ∪ Pc ∪ Pl) generated by vertices in extreme cycles (Pec), by vertices in cycles without exits (Pc), and by line points (Pl) will be a dense ideal in some cases, for instance in the finite one or, more generally, if every vertex connects to Pl ∪ Pc ∪ Pec. Hence its structure will contain much of the information about the Leavitt path algebra. In the row-finite case, we will need to add a new hereditary set: the set of vertices whose tree has infinite bifurcations (Pb∞). Corrales García, María G.Wed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449682016On the Galois correspondence theorem in separable Hopf Galois theory
http://ddd.uab.cat/record/144967
In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure. Crespo, TeresaWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449672016Upper bound for multi-parameter iterated commutators
http://ddd.uab.cat/record/144966
We show that the product BMO space can be characterized by iterated commutators of a large class of Calderón-Zygmund operators. This result followsfrom a new proof of boundedness of iterated commutators in terms of the BMO norm of their symbol functions, using Hytönen's representation theorem of Calderón-Zygmund operators as averages of dyadic shifts. The proof introduces some new paraproducts which have BMO estimates. Dalenc, LaurentWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449662016Mixed norm estimates for the Riesz transforms on SU (2)
http://ddd.uab.cat/record/144965
In this paper we prove mixed norm estimates for Riesz transforms on the group SU(2). From these results vector valued inequalities for sequences of Riesz transforms associated to Jacobi differential operators of different types are deduced. Boggarapu, PradeepWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449652016Fine gradings on e6
http://ddd.uab.cat/record/144964
There are fourteenfine gradings on the exceptional Lie algebra e6 over an algebraically closed field of zero characteristic. We provide their descriptions and a proof that any fine grading is equivalent to one of them. Draper Fontanals, CristinaWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449642016Geometric characterizations of p-Poincaré inequalities in the metric setting
http://ddd.uab.cat/record/144963
We prove that a locally complete metric space endowed with a doubling measure satisfies an ∞-Poincar´e inequality if and only if given a null set, every two points can be joined by a quasiconvex curve which "almost avoids" that set. As an application, we characterize doubling measures on R satisfying an ∞-Poincaré inequality. For Ahlfors Q-regular spaces, we obtain a characterization of p-Poincaré inequality for p > Q in terms of the p-modulus of quasiconvex curves connecting pairs of points in the space. A related characterization is given for the case Q − 1 < p ≤ Q. Durand-Cartagena, EstibalitzWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449632016Nilpotent groups of class three and braces
http://ddd.uab.cat/record/144962
New constructions of braces on finite nilpotent groups are given and hence this leads to new solutions of the Yang–Baxter equation. In particular, it follows that if a group G of odd order is nilpotent of class three, then it is a homomorphic image of the multiplicative group of a finite left brace (i. e. an involutive Yang–Baxter group) which also is a nilpotent group of class three. We give necessary and sufficient conditions for an arbitrary group H to be the multiplicative group of a left brace such that [H, H] ⊆ Soc(H) and H/[H, H] is a standard abelian brace, where Soc(H) denotes the socle of the brace H. Cedó, FerranWed, 23 Dec 2015 07:06:30 GMThttp://ddd.uab.cat/record/1449622016A nonlocal 1-Laplacian problem and median values
http://ddd.uab.cat/record/144961
In this paper, we study solutions to a nonlocal 1-Laplacian equation. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled. Mazón, José M.Wed, 23 Dec 2015 07:06:30 GMThttp://ddd.uab.cat/record/1449612016Nonlocal elliptic equations in bounded domains :: a survey
http://ddd.uab.cat/record/144960
In this paper we survey some results on the Dirichlet problem for nonlocal operators of the form. We start from the very basics, proving existence of solutions, maximum principles, and constructing some useful barriers. Then, we focus on the regularity properties of solutions, both in the interior and on the boundary of the domain. In order to include some natural operators L in the regularity theory, we do not assume any regularity on the kernels. This leads to some interesting features that are purely nonlocal, in the sense that they have no analogue for local equations. We hope that this survey will be useful for both novel and more experienced researchers in the field. Ros-Oton, XavierWed, 23 Dec 2015 07:06:30 GMThttp://ddd.uab.cat/record/1449602016Inequalities for poisson integrals with slowly growing dimensional constants
http://ddd.uab.cat/record/138626
Let Pt be the Poisson kernel. We study the following Lp inequality for the Poisson integral P f(x, t) = (Pt ∗ f)(x) with respect to a Carleson measure µ: L p(R n+1 + ,dµ) ≤ cp,nκ(µ) 1 p L p(Rn,dx) , where 1 < p < ∞ and κ(µ) is the Carleson norm of µ. It was shown by Verbitsky [V] that for p > 2 the constant cp,n can be taken to be independent of the dimension n. We show that c2,n = O((log n) 1 2 ) and that cp,n = O(n 1 p − 1 2 ) for 1 < p < 2 as n → ∞. We observe that standard proofs of this inequality rely on doubling properties of cubes and lead to a value of cp,n that grows exponentially with n. P f. Grafakos, LoukasThu, 01 Oct 2015 08:21:35 GMThttp://ddd.uab.cat/record/1386262007Monoid rings that are firs
http://ddd.uab.cat/record/138535
It is well-known that the monoid ring of the free product of a free group and a free monoid over a skew field is a fir. We give a proof of this fact that is more direct than the proof in the literature. Pitarch, AndreuWed, 30 Sep 2015 14:59:01 GMThttp://ddd.uab.cat/record/1385351990Some remarks on almost finitely generated nilpotent groups
http://ddd.uab.cat/record/138533
We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp = Hp for all p. Then we have proper set-inclusions {fg} C {fg-like} C {fgp}. We examine the extent to which fg-hke nilpotent groups satisfy the axioms for a Serre class. We obtain a complete answer only in the case that [G, G] is finite . (The collection of fgp nilpotent groups is known te form a Serre class in the extended sense). Hilton, PeterWed, 30 Sep 2015 14:43:11 GMThttp://ddd.uab.cat/record/1385331992The fall of the doubling condition in Calderón-Zygmund theory
http://ddd.uab.cat/record/138529
The most important results of standard Calderón-Zygmund Theory have recently been extended to very general non-homogeneous contexts. In this survey paper we describe these extensions and their striking applications to removability problems for bounded analytic functions. We also discuss some of the techniques that allow us to dispense with the doubling condition in dealing with singular integrals. Special attention is paid to the Cauchy Integral. Verdera, JoanWed, 30 Sep 2015 12:09:28 GMThttp://ddd.uab.cat/record/1385292002Multilinear singular integrals
http://ddd.uab.cat/record/138528
We survey the thoery of multilinear singular integral operators with modulation symmetry. The basic example for this theory is the bilinear Hilbert transform and its multilinear variants. We outline a proof of boundedness of Carleson’s operator which shows the close connection of this operator to multilinear singular integrals. We discuss particular multilinear singular integrals which historically arose in the study of eigenfunctions of Schrödinger operators. Thiele, Christoph M.Wed, 30 Sep 2015 12:01:30 GMThttp://ddd.uab.cat/record/1385282002