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1.
Donald I. Cartwright Gabriella Kuhn 《Transactions of the American Mathematical Society》2001,353(5):2073-2090
Let be the group of automorphisms of a homogeneous tree and let be the tensor product of two spherical irreducible unitary representations of . We complete the explicit decomposition of commenced in part I of this paper, by describing the discrete series representations of which appear as subrepresentations of .
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A. V. Rozhkov 《Mathematical Notes》1996,60(2):165-174
The lower central series of the Grigorchuk 3-generated 2-group is described; the indices of the factors of this series are calculated. The nilpotent length and solvability length of the factors by congruence subgroups are determined.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 225–237, August, 1996. 相似文献
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Ghislain R. Franssens 《Mathematical Methods in the Applied Sciences》2011,34(6):703-727
The set of Associated Homogeneous Distributions (AHDs) on R, ??′(R), consists of distributional analogues of power‐log functions with domain in R. This set contains the majority of the (one‐dimensional) distributions typically encountered in physics applications. In earlier work of the author it was shown that ??′(R) admits a closed convolution structure, provided that critical convolution products are defined by a functional extension process. In this paper, the general convolution product formula is derived. Convolution of AHDs on R is found to be associative, except for critical triple products. Critical products are shown to be non‐associative in a minimal and interesting way. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
4.
Ghislain R. Franssens 《Mathematical Methods in the Applied Sciences》2011,34(12):1460-1471
The set of associated homogeneous distributions (AHDs) on R, ??′(R), consists of the distributional analogues of power‐log functions with domain in R. This set contains the majority of the (one‐dimensional) distributions one typically encounters in physics applications. The recent work done by the author showed that the set ??′(R) admits a closed convolution structure (??′(R), *). By combining this structure with the generalized convolution theorem, a distributional multiplication product was defined, resulting in also a closed multiplication structure (??′(R), .). In this paper, the general multiplication product formula for this structure is derived. Multiplication of AHDs on R is associative, except for critical triple products. These critical products are shown to be non‐associative in a simple and interesting way. The non‐associativity is necessary and sufficient to circumvent Schwartz's impossibility theorem on the multiplication of distributions. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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XU Yichao CHEN Minru & MA Songya Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China College of Mathematics Information Sciences Henan University Kaifeng China 《中国科学A辑(英文版)》2006,49(10):1392-1404
We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso(D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F). In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN, F)) and Iso(D(VN,F))(0), where G(0) is the unit connected component of the Lie group G. 相似文献
7.
Jih-Hsin Cheng 《Proceedings of the American Mathematical Society》2000,128(6):1825-1832
We establish Bochner-type formulas for operators related to automorphisms and spherical structures. From such formulas, we draw conclusions about rigidity by making assumptions on the Tanaka-Webster curvature and torsion.
8.
Steven P. Lalley Thomas M. Sellke 《Bulletin of the Brazilian Mathematical Society》2002,33(3):341-350
The contact process on a homogeneous tree of degree 3 or larger is known to have two survival phases: weak and strong. In
the weak survival phase, the "Malthusian parameter" (the Hausdorff dimension of the set of ends of the tree in which the infection
survives) is less than half the Hausdorff dimension of the entire boundary. It is shown that if the expected infection time
of a vertex is bounded by a constant times the probability of infection, then the critical exponent for the Malthusian parameter
is at least 1/2.
Received: 30 June 2002 相似文献
9.
Alexander Dvorsky 《Journal of Functional Analysis》2003,201(2):430-456
In this paper we construct a family of small unitary representations for real semisimple Lie groups associated with Jordan algebras. These representations are realized on L2-spaces of certain orbits in the Jordan algebra. The representations are spherical and one of our key results is a precise L2-estimate for the Fourier transform of the spherical vector. We also consider the tensor products of these representations and describe their decomposition. 相似文献
10.
Guo-mao Wang 《高校应用数学学报(英文版)》2008,23(3):303-312
The purpose of this paper is to investigate the mean size formula of wavelet packets (wavelet subdivision tree) on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree. 相似文献
11.
Wolfgang Woess 《Monatshefte für Mathematik》1995,120(1):55-72
Consider a closed subgroup of the automorphism group of a homogeneous treeT, and assume that acts transitively on the vertex set. Suppose that is a probability measure on which has continuous density with respect to Haar measure and whose support is compact open and generates as a closed semigroup. It is shown that the Martin boundary of with respect to the random walk with law coincides with the space of ends ofT. This extends known results for free groups and applies, for example, to the affine group over a non archimedean local field. 相似文献
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We present two subdivision schemes for the fair discretization of the spherical motion group. The first one is based on the subdivision of the 600-cell according to the tetrahedral/octahedral subdivision scheme in [S. Schaefer, J. Hakenberg, J. Warren, Smooth subdivision of tetrahedral meshes, in: R. Scopigno, D. Zorin (Eds.), Eurographics Symposium on Geometry Processing, 2004, pp. 151–158]. The second presented subdivision scheme is based on the spherical kinematic mapping. In the first step we discretize an elliptic linear congruence by the icosahedral discretization of the unit sphere. Then the resulting lines of the elliptic three-space are discretized such that the difference in the maximal and minimal elliptic distance between neighboring grid points becomes minimal. 相似文献
15.
Adrien Joseph 《Random Structures and Algorithms》2011,39(2):247-274
We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behavior of the shattering times, defined as the first instants when all the blocks of the partition process have cardinality less than a fixed integer. Our results may be applied to the study of certain random split trees. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 247‐274, 2011 相似文献
16.
Henrik Stetkær 《Journal of Functional Analysis》2007,252(1):1-33
We extend results on square integrable representations of a locally compact group to subrepresentations of a representations induced from a character of a closed subgroup. We do so working in the framework of quotient representations of ∗-algebras. 相似文献
17.
The solvability of the equation a1a2 … ak = x2, a1, a2, …, ak ε
is studied for fixed k and ‘dense’ sets
of positive integers. In particular, it is shown that if k is even and k 4, and
is of positive upper density, then this equation can be solved. 相似文献
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Weicai Peng Weiguo Yang Bei Wang 《Journal of Mathematical Analysis and Applications》2010,361(2):293-301
By constructing a non-negative martingale on a homogeneous tree, a class of small deviation theorems for functionals of random fields, the strong law of large numbers for the frequencies of occurrence of states and ordered couple of states for random fields, and the asymptotic equipartition property (AEP) for finite random fields are established. As corollary, the strong law of large numbers and the AEP for Markov chains indexed by a Cayley tree is obtained. Some known results are generalized in this paper. 相似文献
20.
I. V. Shirokov 《Siberian Mathematical Journal》2007,48(6):1127-1140
We demonstrate that the invariant operators on a homogeneous space generate differential invariants and invariant differentiation operators. The coordinate-free method of this article makes it possible to simply the computations essentially, namely to reduce them to operations of linear algebra. Some examples are exhibited. 相似文献