共查询到20条相似文献,搜索用时 8 毫秒
1.
Kaoru Hiraga Atsushi Ichino Tamotsu Ikeda 《Journal of the American Mathematical Society》2008,21(1):283-304
We give a conjectural formula for the formal degree of a discrete series representation in terms of the adjoint -factor. Our conjecture is supported by various examples and is compatible with the Weyl dimension formula. Using twisted endoscopy, we also verify the conjecture for a stable discrete series representation of over a non-archimedean local field of characteristic zero.
2.
Nicolas Burq Gilles Lebeau Fabrice Planchon 《Journal of the American Mathematical Society》2008,21(3):831-845
We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on for any smooth (compact) domain . The main ingredient in the proof is an spectral projector estimate, obtained recently by Smith and Sogge, combined with a precise study of the boundary value problem.
3.
Niels Lauritzen Ulf Raben-Pedersen Jesper Funch Thomsen 《Journal of the American Mathematical Society》2006,19(2):345-355
We prove that Schubert varieties are globally -regular in the sense of Karen Smith. We apply this result to the category of equivariant and holonomic -modules on flag varieties in positive characteristic. Here recent results of Blickle are shown to imply that the simple -modules coincide with local cohomology sheaves with support in Schubert varieties. Using a local Grothendieck-Cousin complex, we prove that the decomposition of local cohomology sheaves with support in Schubert cells is multiplicity free.
4.
J. Marshall Ash Stefan Catoiu 《Transactions of the American Mathematical Society》2008,360(2):959-987
For , a one-parameter family of symmetric quantum derivatives is defined for each order of differentiation as are two families of Riemann symmetric quantum derivatives. For , symmetrization holds, that is, whenever the th Peano derivative exists at a point, all of these derivatives of order also exist at that point. The main result, desymmetrization, is that conversely, for , each symmetric quantum derivative is a.e. equivalent to the Peano derivative of the same order. For and , each th symmetric quantum derivative coincides with both corresponding th Riemann symmetric quantum derivatives, so, in particular, for and , both th Riemann symmetric quantum derivatives are a.e. equivalent to the Peano derivative.
5.
Lisa Orloff Clark Astrid an Huef 《Proceedings of the American Mathematical Society》2008,136(2):623-634
Suppose is a second countable, locally compact, Hausdorff, principal groupoid with a fixed left Haar system. We define a notion of integrability for groupoids and show is integrable if and only if the groupoid -algebra has bounded trace.
6.
Amit Kulshrestha R. Parimala 《Transactions of the American Mathematical Society》2008,360(3):1193-1221
Let be a field of characteristic not whose virtual cohomological dimension is at most . Let be a semisimple group of adjoint type defined over . Let denote the normal subgroup of consisting of elements -equivalent to identity. We show that if is of classical type not containing a factor of type , . If is a simple classical adjoint group of type , we show that if and its multi-quadratic extensions satisfy strong approximation property, then . This leads to a new proof of the -triviality of -rational points of adjoint classical groups defined over number fields.
7.
Let be a random -CNF formula formed by selecting uniformly and independently out of all possible -clauses on variables. It is well known that if , then is unsatisfiable with probability that tends to 1 as . We prove that if , where , then is satisfiable with probability that tends to 1 as .
Our technique, in fact, yields an explicit lower bound for the random -SAT threshold for every . For our bounds improve all previously known such bounds.
8.
Masayuki Asaoka 《Proceedings of the American Mathematical Society》2008,136(2):677-686
For any manifold of dimension at least three, we give a simple construction of a hyperbolic invariant set that exhibits -persistent homoclinic tangency. It provides an open subset of the space of -diffeomorphisms in which generic diffeomorphisms have arbitrary given growth of the number of attracting periodic orbits and admit no symbolic extensions.
9.
Christopher B. Croke 《Proceedings of the American Mathematical Society》2008,136(2):715-717
We consider Riemannian metrics on the -sphere for such that the distance between any pair of antipodal points is bounded below by 1. We show that the volume can be arbitrarily small. This is in contrast to the -dimensional case where Berger has shown that .
10.
In this paper we investigate spline wavelets on general triangulations. In particular, we are interested in wavelets generated from piecewise quadratic polynomials. By using the Powell-Sabin elements, we set up a nested family of spaces of quadratic splines, which are suitable for multiresolution analysis of Besov spaces. Consequently, we construct wavelet bases on general triangulations and give explicit expressions for the wavelets on the three-direction mesh. A general theory is developed so as to verify the global stability of these wavelets in Besov spaces. The wavelet bases constructed in this paper will be useful for numerical solutions of partial differential equations.
11.
Christopher J. Bishop Hrant Hakobyan 《Proceedings of the American Mathematical Society》2008,136(7):2453-2461
The central set of a domain is the set of centers of maximal discs in . Fremlin proved that the central set of a planar domain has zero area and asked whether it can have Hausdorff dimension strictly larger than . We construct a planar domain with central set of Hausdorff dimension .
12.
Pedro L. Q. Pergher 《Proceedings of the American Mathematical Society》2008,136(5):1855-1860
We describe the equivariant cobordism classification of smooth actions of the group , considered as the group generated by two commuting involutions, on closed smooth -dimensional manifolds , for which the fixed point set of the action is a connected manifold of dimension and or . For , the classification is known.
13.
Marcos P. A. Cavalcante 《Proceedings of the American Mathematical Society》2008,136(1):287-294
In this paper we give sufficient conditions for a bounded domain in an -minimal hypersurface of the Euclidean space to be -stable. The Gauss-Kronecker curvature of this hypersurface may be zero on a set of capacity zero.
14.
Mark Hovey 《Transactions of the American Mathematical Society》2008,360(1):369-382
Morava -theory is a much-studied theory in algebraic topology, but it is not a homology theory in the usual sense, because it fails to preserve coproducts (resp. filtered homotopy colimits). The object of this paper is to construct a spectral sequence to compute the Morava -theory of a coproduct (resp. filtered homotopy colimit). The -term of this spectral sequence involves the derived functors of direct sum (resp. filtered colimit) in an appropriate abelian category. We show that there are at most (resp. ) of these derived functors. When , we recover the known result that homotopy commutes with an appropriate version of direct sum in the -local stable homotopy category.
15.
We introduce a new technique that is used to show that the complex projective plane blown up at 6, 7, or 8 points has infinitely many distinct smooth structures. None of these smooth structures admits smoothly embedded spheres with self-intersection , i.e., they are minimal. In addition, none of these smooth structures admits an underlying symplectic structure. Shortly after the appearance of a preliminary version of this article, Park, Stipsicz, and Szabo used the techniques described herein to show that the complex projective plane blown up at 5 points has infinitely many distinct smooth structures. In the final section of this paper we give a construction of such a family of examples.
16.
Alexandru D. Ionescu Stephen Wainger 《Journal of the American Mathematical Society》2006,19(2):357-383
We prove that if is a Calderón-Zygmund kernel and is a polynomial of degree with real coefficients, then the discrete singular Radon transform operator extends to a bounded operator on , . This gives a positive answer to an earlier conjecture of E. M. Stein and S. Wainger.
17.
Ahmet Beyaz 《Transactions of the American Mathematical Society》2008,360(8):4409-4424
This paper provides a topological method to construct all simply-connected, spin, smooth -manifolds with torsion-free homology using simply-connected, smooth -manifolds as building blocks. We explicitly determine the invariants that classify these -manifolds from the intersection form and specific homology classes of the -manifold building blocks.
18.
Wael Abu-Shammala Alberto Torchinsky 《Proceedings of the American Mathematical Society》2008,136(5):1743-1748
In this paper we consider the spaces that lie between and . We discuss their interpolation properties and the behavior of maximal functions and singular integrals acting on them.
19.
20.
Luc Lapointe Jennifer Morse 《Transactions of the American Mathematical Society》2008,360(4):2021-2040
We prove that structure constants related to Hecke algebras at roots of unity are special cases of -Littlewood-Richardson coefficients associated to a product of -Schur functions. As a consequence, both the 3-point Gromov-Witten invariants appearing in the quantum cohomology of the Grassmannian, and the fusion coefficients for the WZW conformal field theories associated to are shown to be -Littlewood-Richardson coefficients. From this, Mark Shimozono conjectured that the -Schur functions form the Schubert basis for the homology of the loop Grassmannian, whereas -Schur coproducts correspond to the integral cohomology of the loop Grassmannian. We introduce dual -Schur functions defined on weights of -tableaux that, given Shimozono's conjecture, form the Schubert basis for the cohomology of the loop Grassmannian. We derive several properties of these functions that extend those of skew Schur functions.