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1.
We prove an extension of Hardy's classical characterization of real Gaussians of the form , , to the case of complex Gaussians in which is a complex number with positive real part. Such functions represent rotations in the complex plane of real Gaussians. A condition on the rate of decay of analytic extensions of a function and its Fourier transform along some pair of lines in the complex plane is shown to imply that is a complex Gaussian.
2.
In this paper we classify the subsemigroups of any connected semisimple Lie groupG which areK-bi-invariant, whereG=KAN is an Iwasawa decomposition ofG. 相似文献
3.
In this article, we prove a heat kernel version of Hardy’s theorem for the Laguerre hypergroup. 相似文献
4.
Susana A. Salamanca-Riba 《Proceedings of the American Mathematical Society》1997,125(10):3107-3117
In this paper we prove that a unitary representation of whose infinitesimal character satisfies some regularity condition is infinitesimally isomorphic to an module. This is done using similar techniques as those used by the author in earlier work.
5.
Ming Liao 《Transactions of the American Mathematical Society》1998,350(2):501-522
We study the asymptotic stability of stochastic flows on compact spaces induced by Levy processes in semisimple Lie groups. It is shown that the Lyapunov exponents can be determined naturally in terms of root structure of the Lie group and there is an open subset whose complement has a positive codimension such that, after a random rotation, each of its connected components is shrunk to a single moving point exponentially under the flow.
6.
A. I. Shtern 《Mathematical Notes》2006,80(3-4):435-441
It is proved that an arbitrary pseudocharacter on a semisimple Lie group is continuous. 相似文献
7.
Shripad M. Garge 《Proceedings Mathematical Sciences》2005,115(4):411-427
The aim of this paper is to investigate the order coincidences among the finite semisimple groups and to give a reasoning
of such order coincidences through the transitive actions of compact Lie groups.
It is a theorem of Artin and Tits that a finite simple group is determined by its order, with the exception of the groups
(A3(2), A2(4)) and(B
n
(q), C
n
(q)) forn ≥ 3,q odd. We investigate the situation for finite semisimple groups of Lie type. It turns out that the order of the finite
group H(
) for a split semisimple algebraic groupH defined over
, does not determine the groupH up to isomorphism, but it determines the field
under some mild conditions. We then put a group structure on the pairs(H
1,H
2) of split semisimple groups defined over a fixed field
such that the orders of the finite groups H1(
) and H2(
) are the same and the groupsH
i
have no common simple direct factors. We obtain an explicit set of generators for this abelian, torsion-free group. We finally
show that the order coincidences for some of these generators can be understood by the inclusions of transitive actions of
compact Lie groups. 相似文献
8.
In this article, we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed
to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct
the first known examples of harmonic morphisms from the non-compact Lie groups , SU
*(2n), , SO
*(2n), SO(p, q), SU(p, q) and Sp(p, q) equipped with their standard dual semi-Riemannian metrics.
相似文献
9.
Mamoru Mimura Tetsu Nishimoto 《Proceedings of the American Mathematical Society》2002,130(8):2451-2459
The present note is to give a cellular decomposition of the compact connected exceptional Lie group .
10.
Anthony H. Dooley Genkai Zhang 《Proceedings of the American Mathematical Society》1997,125(9):2779-2787
We consider certain induced representations of the group
realized on line bundles over the projective space of . We calculate the intertwining operators in the compact picture. We find all the unitarizable representations and determine the invariant norm.
realized on line bundles over the projective space of . We calculate the intertwining operators in the compact picture. We find all the unitarizable representations and determine the invariant norm.
11.
A widely used result of Wedderburn and Artin states that “every left ideal of a ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct product of matrix rings over division rings.” Motivated by this, we call a module M virtually semisimple if every submodule of M is isomorphic to a direct summand of M and M is called completely virtually semisimple if every submodule of M is virtually semisimple. We show that the left R-module R is completely virtually semisimple if and only if R has a unique decomposition as a finite direct product of matrix rings over principal left ideal domains. This shows that R is completely virtually semisimple on both sides if and only if every finitely generated (left and right) R-module is a direct sum of a singular module and a projective virtually semisimple module. The Wedderburn-Artin theorem follows as a corollary from our result. 相似文献
12.
Carles Broto Jesper M. Mø ller 《Transactions of the American Mathematical Society》2001,353(11):4461-4479
We show that there is only one embedding of in at the prime , up to self-maps of . We also describe the effect of the group of self-equivalences of at the prime on this embedding and then show that the Friedlander exceptional isogeny composed with a suitable Adams map is an involution of whose homotopy fixed point set coincide with
13.
People studied the properties and structures of restricted Lie algebras all whose elements are semisimple. It is the main
objective of this paper to continue the investigation in order to obtain deeper structure theorems. We obtain some sufficient
conditions for the commutativity of restricted Lie algebras, generalize some results of R. Farnsteiner and characterize some
properties of a finite-dimensional semisimple restricted Lie algebra all whose elements are semisimple. Moreover, we show
that a centralsimple restricted Lie algebra all whose elements are semisimple over a field of characteristic p > 7 is a form of a classical Lie algebra. 相似文献
14.
Sergey Fomin Andrei Zelevinsky 《Proceedings of the American Mathematical Society》2000,128(12):3749-3759
We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F. R. Gantmacher, M. G. Krein, A. Whitney, C. Loewner, M. Gasca, and J. M. Peña to the case of an arbitrary complex semisimple Lie group. 相似文献
15.
William H Barker 《Journal of Functional Analysis》1975,20(3):179-207
Let G be a connected semisimple Lie group with finite center and K a maximal compact subgroup. Denote (i) Harish-Chandra's Schwartz spaces by p(G)(0<p?2), (ii) the K-biinvariant elements in p(G) by p(G), (iii) the positive definite (zonal) spherical functions by , and (iv) the spherical transform on p(G) by ? → gj. For T a positive definite distribution on G it is established that (i) T extends uniquely onto l(G), (ii) there exists a unique measure μ of polynomial growth on such that T[ψ]=∫pψdμ for all ψ?I1(G) (iii) all measures μ of polynomial growth on are obtained in this way, and (iv) T may be extended to a particular p(G) space (1 ? p ? 2) if and only if the support of μ lies in a certain easily defined subset of . These results generalize a well-known theorem of Godement, and the proofs rely heavily on the recent harmonic analysis results of Trombi and Varadarajan. 相似文献
16.
András Domokos Roland EsquerraBob Jaffa Tom Schulte 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4642-4652
In this paper, we consider a natural subelliptic structure in semisimple, compact and connected Lie groups, and estimate the constant in the so-called subelliptic Friedrichs-Knapp-Stein inequality, which has implications in the regularity theory of p-energy minimizers. 相似文献
17.
José Garcí a-Cuerva José Manuel Marco Javier Parcet 《Transactions of the American Mathematical Society》2003,355(9):3591-3609
Sharp Fourier type and cotype of Lebesgue spaces and Schatten classes with respect to an arbitrary compact semisimple Lie group are investigated. In the process, a local variant of the Hausdorff-Young inequality on such groups is given.
18.
S. G. Dani 《Journal of Theoretical Probability》1991,4(3):625-629
We give here a characterization of the Cauchy-type distributions onG/P, whereG is a semisimple Lie group andP is a parabolic subgroup. 相似文献
19.
Pham Huu Tiep A. E. Zalesskii 《Proceedings of the American Mathematical Society》2002,130(11):3177-3184
Let be a finite group of Lie type in characteristic . This paper addresses the problem of describing the irreducible complex (or -adic) representations of that remain absolutely irreducible under the Brauer reduction modulo . An efficient approach to solve this problem for 3$">has been elaborated in earlier papers by the authors. In this paper, we use arithmetical properties of character degrees to solve this problem for the groups
provided that . We also prove an asymptotical result, which solves the problem for all finite groups of Lie type over with large enough.
provided that . We also prove an asymptotical result, which solves the problem for all finite groups of Lie type over with large enough.
20.
Thierry Levasseur 《Proceedings of the American Mathematical Society》2002,130(12):3519-3523
Let be a complex semisimple Lie algebra and be its enveloping algebra. We deduce from the work of R. Bezrukavnikov, A. Braverman and L. Positselskii that the Krull-Gabriel-Rentschler dimension of is equal to the dimension of a Borel subalgebra of .