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1.
We provide new arguments to see topological Kac-Moody
groups as generalized semisimple groups over local fields: they are products
of topologically simple groups and their Iwahori subgroups are the normalizers
of the pro-p Sylow subgroups. We use a dynamical characterization
of parabolic subgroups to prove that some countable Kac-Moody groups
with Fuchsian buildings are not linear. We show for this that the linearity
of a countable Kac-Moody group implies the existence of a closed embedding
of the corresponding topological group in a non-Archimedean simple
Lie group, thanks to a commensurator super-rigidity theorem proved in
the Appendix by P. Bonvin. 相似文献
2.
We show that the unitary group of a separable Hilbert space has
Kazhdan's Property (T), when it is equipped with the strong operator
topology. More precisely, for every integer m
2, we give an
explicit Kazhdan set consisting of m unitary operators and determine
an optimal Kazhdan constant for this set. Moreover, we show that a
locally compact group with Kazhdan's Property (T) has a finite Kazhdan
set if and only if its Bohr compactification has a finite Kazhdan
set. As a consequence, if a locally compact group with Property (T)
is minimally almost periodic, then it has a finite Kazhdan set. 相似文献
3.
Let be a group generated by a finite set S. We give a sufficient
condition for to have Kazhdan's property (T). This condition is
easy to check and gives Kazhdan constants. We give examples of
groups to which this method applies. We prove that in some setting
generic presentations define groups which satisfy this condition and
thus have property (T). Moreover we prove that small changes in the
presentation of a group satisfying this condition do not change the
fact that the group has property (T). 相似文献
4.
5.
6.
7.
We show that germs of local real-analytic CR automorphisms of a
real-analytic hypersurface M in
$\mathbb{C}$2 at a point
p M
are uniquelydetermined by their jets of some finite order at
p if and only if M is
not Levi-flat near p. This seems to be the first necessary and sufficient
result on finite jet determination and the first result of this kind in
the infinite type case.If M is of finite type at p,
we prove a stronger assertion: the local real-analytic
CR automorphisms of M fixing p
are analytically parametrized (and hence uniquely determined)
by their 2-jets at p.
This result is optimal since the automorphisms of the unit sphere are
not determined by their 1-jets at a point of the sphere. The finite
type condition is necessary since otherwise the needed jet order can
be arbitrarily high [Kow1,2], [Z2]. Moreover, we show, by an example,
that determination by 2-jets fails for finite type hypersurfaces already
in $\mathbb{C)$3.We also give an application to the dynamics of germs of local
biholomorphisms of $\mathbb{C)$2. 相似文献
8.
We study the Dirac operators on the half-line. If the potential
is square summable, we prove existence of the wave operators. 相似文献
9.
10.
We develop an operator approach to the problem named in the title.
It is based on operator treatment of some relations between Bessel functions,
and hypergeometric functions as well. Our operator version of the Delsarte-
Povzner formulas also plays an essential role in the paper. 相似文献
11.
In this paper, we prove that the linearized elasticity system has
no eigenvalues in two geometric situations: the whole space
and a local perturbation of the half-space. We consider the Lamé coefficients and the
density varying in an unbounded part of the domain. For the whole space,
we use the operations curl and div
to reduce our system to a scalar problem
and use a limiting absorption principle for the reduced scalar equation
given by the partial Fourier transform. For the perturbed half-space, this
decompositions being no longer valid, we give an other method based on a
pseudo-decomposition using the operations div
and curl in the horizontal
direction. In contrast to the whole space case, the reduced problems depend
strongly on the dual Fourier variable which do not enable us to use same
techniques. To study these reduced problems, we use the analytic theory of
linear operators. 相似文献
12.
B. Osilenker 《Analysis Mathematica》1998,24(1):293-310
An analog of the trace formula for orthogonal polynomials with asymptotically 2-periodic recurrence coefficients is given. This result is based on the representation of the Fejér kernel for the system. 相似文献
13.
14.
The involutions in this paper are algebra anti-automorphisms of period two. Involutions on endomorphism algebras of finite-dimensional
vector spaces are adjoint to symmetric or skew-symmetric bilinear forms, or to hermitian forms. Analogues of the classical
invariants of quadratic forms (discriminant, Clifford algebra, signature) have been defined for arbitrary central simple algebras
with involution. In this paper it is shown that over certain fields these invariants are sufficient to classify involutions
up to conjugation. For algebras of low degree a classification is obtained over an arbitrary field.
Received: 29 April 1999 相似文献
15.
16.
Hervé Jacquet 《Israel Journal of Mathematics》1995,89(1-3):1-59
LetE/F be a quadratic extension of number fields,G the group GL(3,E) regarded as an algebraic group overF andU a quasi-split unitary group in three variables. Let alsoϑ be a generic character of a maximal unipotent subgroupN ofG. We derive an explicit expression for the integral
whereK
cont is the continuous part of the kernel attached to a smooth function of compact support onG(A). In particular, we prove that this expression is absolutely convergent. The result can be used to show that a cuspidal representation
ofG contains a vectorφ such thatεφ(u)du≠0 if and only if it is a base change from a representation of GL(3,F).
Partially supported by NSF Grant DMS-91-01637. 相似文献
17.
18.
Ruan Jiong 《数学年刊B辑(英文版)》1982,3(3):261-272
本文中我们考虑下面的系统
$[\frac{{dx(t)}}{{dt}} = L({x_i}) + Rf(\sigma (t))\]$
$[\sigma (t) = Cx(t)\]$
以及
$[\frac{{dx(t)}}{{dt}} = L({x_i}) + Rf(\sigma (t))\]$
$[\frac{{d\xi (t)}}{{dt}} = f(\sigma (t)),\sigma (t) = Cx(t) + D\xi (t)\]$
其中x,f是n维向量,\sigma,\xi 是m维向量,C、D是m*n矩阵,R是n*m矩阵,m>1.
我们引入了系统的广义H-绝对稳定性,并给出了系统(1)(2)的广义H-绝对稳定性的充分判据。本文中我们推广和简化了文[1,2]中的方法。对非线性项f(\sigma)去掉了f_j仅依赖于\sigma_j的限制。 相似文献
19.
Annette Huber 《Mathematische Nachrichten》2008,281(12):1764-1776
We clarify the expected properties of the slice filtration on triangulated motives from the point of view of the generalized Hodge conjecture. In the appendix, J. Ayoub proves unconditionally that the slice filtration does not respect geometric motives. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献