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1.
Joachim Hilgert Karl-Hermann Neeb 《Transactions of the American Mathematical Society》2000,352(3):1345-1380
Let be a simply connected complex Lie group with Lie algebra , a real form of , and the analytic subgroup of corresponding to . The symmetric space together with a -invariant partial order is referred to as an Olshanskii space. In a previous paper we constructed a family of integral spherical functions on the positive domain of . In this paper we determine all of those spherical functions on which are positive definite in a certain sense.
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3.
William Browder Jonathan Pakianathan 《Transactions of the American Mathematical Society》2000,352(6):2659-2688
In this paper we will study the cohomology of a family of -groups associated to -Lie algebras. More precisely, we study a category of -groups which will be equivalent to the category of -bracket algebras (Lie algebras minus the Jacobi identity). We then show that for a group in this category, its -cohomology is that of an elementary abelian -group if and only if it is associated to a Lie algebra.
We then proceed to study the exponent of in the case that is associated to a Lie algebra . To do this, we use the Bockstein spectral sequence and derive a formula that gives in terms of the Lie algebra cohomologies of . We then expand some of these results to a wider category of -groups. In particular, we calculate the cohomology of the -groups which are defined to be the kernel of the mod reduction
4.
We prove that a ()-connected map from a compact PL -manifold to a generalized -manifold with the disjoint disks property, , is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompact and proper maps that are properly ()-connected. The techniques developed lead to a general position result for arbitrary maps , , and a Whitney trick for separating submanifolds of that have intersection number 0, analogous to the well-known results when is a manifold.
5.
Xiaotie She 《Transactions of the American Mathematical Society》1999,351(3):1075-1094
Let be a normalised new form of weight for over and , its base change lift to . A sufficient condition is given for the nonvanishing at the center of the critical strip of infinitely many cubic twists of the -function of . There is an algorithm to check the condition for any given form. The new form of level is used to illustrate our method.
6.
We classify all complex representations of the automorphism group of the free group of dimension Among those representations is a new representation of dimension which does not vanish on the group of inner automorphisms.
7.
Claus Scheiderer 《Transactions of the American Mathematical Society》2000,352(3):1039-1069
Let be an affine algebraic variety over (or any other real closed field ). We ask when it is true that every positive semidefinite (psd) polynomial function on is a sum of squares (sos). We show that for the answer is always negative if has a real point. Also, if is a smooth non-rational curve all of whose points at infinity are real, the answer is again negative. The same holds if is a smooth surface with only real divisors at infinity. The ``compact' case is harder. We completely settle the case of smooth curves of genus : If such a curve has a complex point at infinity, then every psd function is sos, provided the field is archimedean. If is not archimedean, there are counter-examples of genus .
8.
Claude Lemaré chal Franç ois Oustry Claudia Sagastizá bal 《Transactions of the American Mathematical Society》2000,352(2):711-729
At a given point , a convex function is differentiable in a certain subspace (the subspace along which has 0-breadth). This property opens the way to defining a suitably restricted second derivative of at . We do this via an intermediate function, convex on . We call this function the -Lagrangian; it coincides with the ordinary Lagrangian in composite cases: exact penalty, semidefinite programming. Also, we use this new theory to design a conceptual pattern for superlinearly convergent minimization algorithms. Finally, we establish a connection with the Moreau-Yosida regularization.
9.
Jonathan Brundan 《Transactions of the American Mathematical Society》2000,352(3):1405-1436
We classify all pairs of reductive maximal connected subgroups of a classical algebraic group that have a dense double coset in . Using this, we show that for an arbitrary pair of reductive subgroups of a reductive group satisfying a certain mild technical condition, there is a dense -double coset in precisely when is a factorization.
10.
The ``spin' L-function of an automorphic representation of is an Euler product of degree associated with the spin representation of the L-group . If or , and the automorphic representation is generic in the sense of having a Whittaker model, the analytic properties of these L-functions are studied by the Rankin-Selberg method.
11.
Moira A. McDermott 《Transactions of the American Mathematical Society》2000,352(1):95-114
We consider tight closure, plus closure and Frobenius closure in the rings , where is a field of characteristic and . We use a -grading of these rings to reduce questions about ideals in the quotient rings to questions about ideals in the regular ring . We show that Frobenius closure is the same as tight closure in certain classes of ideals when . Since , we conclude that for these ideals. Using injective modules over the ring , the union of all th roots of elements of , we reduce the question of whether for -graded ideals to the case of -graded irreducible modules. We classify the irreducible -primary -graded ideals. We then show that for most irreducible -primary -graded ideals in , where is a field of characteristic and . Hence for these ideals.
12.
Bang-He Li 《Transactions of the American Mathematical Society》2000,352(9):4155-4169
For any nonnegative class in , the minimal genus of smoothly embedded surfaces which represent is given for , and in some cases with , the minimal genus is also given. For the finiteness of orbits under diffeomorphisms with minimal genus , we prove that it is true for with and for with .
13.
Banach spaces with the Daugavet property 总被引:6,自引:0,他引:6
Vladimir M. Kadets Roman V. Shvidkoy Gleb G. Sirotkin Dirk Werner 《Transactions of the American Mathematical Society》2000,352(2):855-873
A Banach space is said to have the Daugavet property if every operator of rank satisfies . We show that then every weakly compact operator satisfies this equation as well and that contains a copy of . However, need not contain a copy of . We also study pairs of spaces and operators satisfying , where is the natural embedding. This leads to the result that a Banach space with the Daugavet property does not embed into a space with an unconditional basis. In another direction, we investigate spaces where the set of operators with is as small as possible and give characterisations in terms of a smoothness condition.
14.
L. J. Ratliff Jr. D. E. Rush Jr. 《Transactions of the American Mathematical Society》2000,352(4):1647-1674
The main theorem characterizes, in terms of bracket powers, analytic spread one ideals in local rings. Specifically, let be regular nonunits in a local (Noetherian) ring and assume that , the integral closure of , where . Then the main result shows that for all but finitely many units in that are non-congruent modulo and for all large integers and it holds that for and not divisible by , where is the -th bracket power of . And, conversely, if there exist positive integers , , and such that has a basis such that , then has analytic spread one.
15.
Roger L. Kraft 《Transactions of the American Mathematical Society》2000,352(3):1315-1328
Let , be Cantor sets embedded in the real line, and let , be their respective thicknesses. If , then it is well known that the difference set is a disjoint union of closed intervals. B. Williams showed that for some , it may be that is as small as a single point. However, the author previously showed that generically, the other extreme is true; contains a Cantor set for all in a generic subset of . This paper shows that small intersections of thick Cantor sets are also rare in the sense of Lebesgue measure; if , then contains a Cantor set for almost all in .
16.
Masataka Nishikawa Kenji Nishihara 《Transactions of the American Mathematical Society》2000,352(3):1203-1215
This paper is concerned with the asymptotic behavior of the solution toward the planar rarefaction wave connecting and for the scalar viscous conservation law in two space dimensions. We assume that the initial data tends to constant states as , respectively. Then, the convergence rate to of the solution is investigated without the smallness conditions of and the initial disturbance. The proof is given by elementary -energy method.
17.
R. M. Bryant Ralph Stö hr 《Transactions of the American Mathematical Society》2000,352(2):901-934
We study the free Lie algebra over a field of non-zero characteristic as a module for the cyclic group of order acting on by cyclically permuting the elements of a free generating set. Our main result is a complete decomposition of as a direct sum of indecomposable modules.
18.
R. Dalmasso 《Transactions of the American Mathematical Society》2000,352(6):2723-2736
A nonempty bounded open set () is said to have the Pompeiu property if and only if the only continuous function on for which the integral of over is zero for all rigid motions of is . We consider a nonempty bounded open set with Lipschitz boundary and we assume that the complement of is connected. We show that the failure of the Pompeiu property for implies some geometric conditions. Using these conditions we prove that a special kind of solid tori in , , has the Pompeiu property. So far the result was proved only for solid tori in . We also examine the case of planar domains. Finally we extend the example of solid tori to domains in bounded by hypersurfaces of revolution.
19.
Huyi Hu 《Transactions of the American Mathematical Society》2000,352(5):2331-2367
A diffeomorphism of a compact manifold is called ``almost Anosov' if it is uniformly hyperbolic away from a finite set of points. We show that under some nondegeneracy condition, every almost Anosov diffeomorphism admits an invariant measure that has absolutely continuous conditional measures on unstable manifolds. The measure is either finite or infinite, and is called SBR measure or infinite SBR measure respectively. Therefore, tends to either an SBR measure or for almost every with respect to Lebesgue measure. ( is the Dirac measure at .) For each case, we give sufficient conditions by using coefficients of the third order terms in the Taylor expansion of at .
20.
Pedro J. Sancho de Salas 《Transactions of the American Mathematical Society》2000,352(2):595-608
Let be a finite field extension and let us consider the automorphism scheme . We prove that is a complete -group, i.e., it has trivial centre and any automorphism is inner, except for separable extensions of degree 2 or 6. As a consequence, we obtain for finite field extensions of , not being separable of degree 2 or 6, the following equivalence: