共查询到20条相似文献,搜索用时 62 毫秒
1.
Eva Curry 《Proceedings of the American Mathematical Society》2006,134(8):2411-2418
We investigate the connection between radix representations for and self-affine tilings of . We apply our results to show that Haar-like multivariable wavelets exist for all dilation matrices that are sufficiently large.
2.
Hermann Koenig Nicole Tomczak-Jaegermann 《Proceedings of the American Mathematical Society》2005,133(4):1213-1221
Using -ellipsoids we prove versions of the inverse Santaló inequality and the inverse Brunn-Minkowski inequality for a general class of measures replacing the usual volume on . This class contains in particular the Gaussian measure on .
3.
Jeremy T. Tyson 《Proceedings of the American Mathematical Society》2000,128(11):3361-3367
For any , there is a compact set of (Hausdorff) dimension whose dimension cannot be lowered by any quasiconformal map . We conjecture that no such set exists in the case . More generally, we identify a broad class of metric spaces whose Hausdorff dimension is minimal among quasisymmetric images.
4.
Tobias Ekholm John Etnyre Michael Sullivan 《Transactions of the American Mathematical Society》2007,359(7):3301-3335
A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form , where is an exact symplectic manifold, is established. The class of such contact manifolds includes 1-jet spaces of smooth manifolds. As an application, contact homology is used to provide (smooth) isotopy invariants of submanifolds of and, more generally, invariants of self transverse immersions into up to restricted regular homotopies. When , this application is the first step in extending and providing a contact geometric underpinning for the new knot invariants of Ng.
5.
In this paper we present an interpolation inequality in the homogeneous Besov spaces on , which reduces to a number of well-known inequalities in special cases.
6.
Curtis T. McMullen 《Journal of the American Mathematical Society》2005,18(3):711-734
Let be the diagonal subgroup, and identify with the space of unimodular lattices in . In this paper we show that the closure of any bounded orbit
meets the set of well-rounded lattices. This assertion implies Minkowski's conjecture for and yields bounds for the density of algebraic integers in totally real sextic fields.
meets the set of well-rounded lattices. This assertion implies Minkowski's conjecture for and yields bounds for the density of algebraic integers in totally real sextic fields.
The proof is based on the theory of topological dimension, as reflected in the combinatorics of open covers of and .
7.
Let be the standard closed positive cone in and let be the set of integers for which there exists a continuous, order preserving, subhomogeneous map , which has a periodic point with period . It has been shown by Akian, Gaubert, Lemmens, and Nussbaum that is contained in the set consisting of those for which there exist integers and such that , , and for some . This note shows that for all .
8.
On commutators of fractional integrals 总被引:1,自引:0,他引:1
Xuan Thinh Duong Li Xin Yan 《Proceedings of the American Mathematical Society》2004,132(12):3549-3557
Let be the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds, and let be the fractional integrals of for . For a BMO function on , we show boundedness of the commutators from to , where . Our result of this boundedness still holds when is replaced by a Lipschitz domain of with infinite measure. We give applications to large classes of differential operators such as the magnetic Schrödinger operators and second-order elliptic operators of divergence form.
9.
Omer Friedland 《Proceedings of the American Mathematical Society》2008,136(10):3639-3645
We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on . This is an application of a small ball estimate and Chernoff's method, that has been recently used in the context of Asymptotic Geometric Analysis.
10.
Frank Sottile Thorsten Theobald 《Proceedings of the American Mathematical Society》2005,133(10):2835-2844
Let and denote the dimension and the degree of the Grassmannian , respectively. For each there are (a priori complex) -planes in tangent to general quadratic hypersurfaces in . We show that this class of enumerative problems is fully real, i.e., for there exists a configuration of real quadrics in (affine) real space so that all the mutually tangent -flats are real.
11.
Prabhu Janakiraman 《Transactions of the American Mathematical Society》2006,358(5):1937-1952
The following limit result holds for the weak-type (1,1) constant of dilation-commuting singular integral operator in : for , , For the maximal operator , the corresponding result is
12.
Jerry R. Muir Jr. Ted J. Suffridge 《Proceedings of the American Mathematical Society》2001,129(11):3389-3393
In this paper, we study univalent holomorphic mappings of the unit ball in that have the property that the image contains a line for some , . We show that under certain rather reasonable conditions, up to composition with a holomorphic automorphism of the ball, the mapping is an extension of the strip mapping in the plane to higher dimensions.
13.
Yu. I. Lyubich 《Proceedings of the American Mathematical Society》2008,136(11):3953-3956
The isometric embeddings (, ) over a field are considered, and an upper bound for the minimal is proved. In the commutative case ( ) the bound was obtained by Delbaen, Jarchow and Pełczyński (1998) in a different way.
14.
Rü diger W. Braun Reinhold Meise B. A. Taylor 《Transactions of the American Mathematical Society》2004,356(4):1315-1383
The local Phragmén-Lindelöf condition for analytic subvarieties of at real points plays a crucial role in complex analysis and in the theory of constant coefficient partial differential operators, as Hörmander has shown. Here, necessary geometric conditions for this Phragmén-Lindelöf condition are derived. They are shown to be sufficient in the case of curves in arbitrary dimension and of surfaces in . The latter result leads to a geometric characterization of those constant coefficient partial differential operators which are surjective on the space of all real analytic functions on .
15.
P. Cifuentes K. S. Kazarian A. San Antolí n 《Proceedings of the American Mathematical Society》2005,133(4):1013-1023
We characterize the scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear map such that and all (complex) eigenvalues of have absolute value greater than In the general case the conditions depend on the map We identify some maps for which the obtained condition is equivalent to the dyadic case, i.e., when is a diagonal matrix with all numbers in the diagonal equal to There are also easy examples of expanding maps for which the obtained condition is not compatible with the dyadic case. The complete characterization of the maps for which the obtained conditions are equivalent is out of the scope of the present note.
16.
Alberto Elduque 《Transactions of the American Mathematical Society》2004,356(10):3963-3983
The centralizer algebra of the action of on the real tensor powers of its natural module, , is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for and with the decomposition of into irreducible submodules is considered.
17.
Karel Dekimpe 《Proceedings of the American Mathematical Society》2003,131(3):973-978
We are dealing with Lie groups which are diffeomorphic to , for some . After identifying with , the multiplication on can be seen as a map . We show that if is a polynomial map in one of the two (sets of) variables or , then is solvable. Moreover, if one knows that is polynomial in one of the variables, the group is nilpotent if and only if is polynomial in both its variables.
18.
Alessandro Tancredi Alberto Tognoli 《Proceedings of the American Mathematical Society》2006,134(4):983-987
We show that the product of any sphere by any compact connected component of a real algebraic variety is Nash isomorphic to a real algebraic variety, and we deduce such a result for some non-compact components, too. It follows also that the product of any sphere by any compact global Nash subvariety of is Nash isomorphic to a real algebraic variety.
19.
Pavel Shvartsman 《Transactions of the American Mathematical Society》2008,360(10):5529-5550
We study a variant of the Whitney extension problem (1934) for the space . We identify with a space of Lipschitz mappings from into the space of polynomial fields on equipped with a certain metric. This identification allows us to reformulate the Whitney problem for as a Lipschitz selection problem for set-valued mappings into a certain family of subsets of . We prove a Helly-type criterion for the existence of Lipschitz selections for such set-valued mappings defined on finite sets. With the help of this criterion, we improve estimates for finiteness numbers in finiteness theorems for due to C. Fefferman.
20.
Petr Holicky Tamá s Keleti 《Proceedings of the American Mathematical Society》2005,133(6):1851-1859
It is known that the sets of extreme and exposed points of a convex Borel subset of are Borel. We show that for there exist convex subsets of such that the sets of their extreme and exposed points coincide and are of arbitrarily high Borel class. On the other hand, we show that the sets of extreme and of exposed points of a convex set of additive Borel class are of ambiguous Borel class . For proving the latter-mentioned results we show that the union of the open and the union of the closed segments of are of the additive Borel class if is a convex set of additive Borel class .