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1.
Donald I. Cartwright 《Monatshefte für Mathematik》2001,133(2):93-109
To any locally finite thick building of type there is naturally associated a commutative algebra of operators. When is constructed from a local field F with local ring , and , then is isomorphic to the convolution algebra of compactly supported bi-K-invariant functions on PGL(n+1,F). We give a proof, valid for any , that the multiplicative functionals on may all be expressed in terms of Hall–Littlewood polynomials. Regarding as a subalgebra of the C
*-algebra of bounded operators on the space of square summable functions on the vertex set of , we find the spectrum of the C
*-algebra , the closure of . This generalizes results obtained in [3] when n = 1 and in [5] when n = 2.
(Received 26 June 2000; in revised form 21 February 2001) 相似文献
2.
For fixed generalized reflection matrix P, i.e. P
T
= P, P
2 = I, then matrix X is said to be generalized bisymmetric, if X = X
T
= PXP. In this paper, an iterative method is constructed to find the generalized bisymmetric solutions of the matrix equation A
1
X
1
B
1 + A
2
X
2
B
2 + ⋯ + A
l
X
l
B
l
= C where [X
1,X
2, ⋯ ,X
l
] is real matrices group. By this iterative method, the solvability of the matrix equation can be judged automatically. When
the matrix equation is consistent, for any initial generalized bisymmetric matrix group , a generalized bisymmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors,
and the least norm generalized bisymmetric solution group can be obtained by choosing a special kind of initial generalized
bisymmetric matrix group. In addition, the optimal approximation generalized bisymmetric solution group to a given generalized
bisymmetric matrix group in Frobenius norm can be obtained by finding the least norm generalized bisymmetric solution group of the new matrix equation
, where . Given numerical examples show that the algorithm is efficient.
Research supported by: (1) the National Natural Science Foundation of China (10571047) and (10771058), (2) Natural Science
Foundation of Hunan Province (06JJ2053), (3) Scientific Research Fund of Hunan Provincial Education Department(06A017). 相似文献
3.
Let K be a field of characteristic 0 and let p, q, G
0
, G
1
, P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G
n
(x))
n=0
∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G
n
(x) = G
m
(P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we
present also bounds for the cardinality of the set
In the last part we specialize our results to certain families of orthogonal polynomials.
This work was supported by the Austrian Science Foundation FWF, grant S8307-MAT.
The second author was supported by the Hungarian National Foundation for Scientific Research Grants No 16741 and 38225.
Received June 5, 2001; in revised form February 26, 2002
RID="a"
ID="a" Dedicated to Edmund Hlawka on the occasion of his 85th birthday 相似文献
4.
Let K be a field of characteristic 0 and let p, q, G 0 , G 1 , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G n (x)) n=0 ∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G n (x) = G m (P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we present also bounds for the cardinality of the set
相似文献
5.
6.
Guyan Robertson 《K-Theory》2001,22(3):251-269
Let be a torsionfree lattice in G=PGL(n+1,
, where n 1 and
is a nonArchimedean local field. Then acts on the Furstenberg boundary G/P, where P is a minimal parabolic subgroup of G. The identity element I in the crossedproduct C
*algebra C(G/P) generates a class [I] in the K
0 group of C(G/P) . It is shown that [I] is a torsion element of K
0 and there is an explicit bound for the order of [I]. The result is proved more generally for groups acting on affine buildings of type Ã
n. For n=1, 2 the Euler–Poincaré characteristic () annihilates the class [I]. 相似文献
7.
We prove that the quasi-Banach spaces 1 (p) and p (1), 0 < p < 1 have a unique unconditional basis up to permutation 相似文献
8.
We prove Lp-spectral independence for generators of C0-semigroups estimated by the positive C0-semigroup . In the preliminary process of the proof, we obtain the asymptotic expansion formula for the integral kernel of the C0-semigroup . 相似文献
9.
B. de Malafosse 《Acta Mathematica Hungarica》2009,122(3):217-230
We deal with the sum of sequence spaces. Then we apply these results to characterize matrix transformations mapping between
s
h,l
(λ, μ) = s
α
0((Δ − λI)
h
) + s
β
(c)((Δ − μI)
l
) and s
γ
. Among other things the aim of this paper is to reduce the set (s
h,l
(λ, μ), s
γ
to a set of the form S
τ,γ
.
相似文献
10.
David Soudry 《Israel Journal of Mathematics》2000,120(1):511-561
In this paper we prove the full multiplicativity (in both variables) of gamma factors for generic representations of SO2ℓ+1 × GL
n
. These gamma factors are initially defined as proportionality factors of local functional equations, derived from a corresponding
global theory of certain Rankin-Selberg integrals which interpolate standardL-functions for SO2ℓ+1 × GL
n
. 相似文献
11.
We classify all connected subgroups of SO(2, n) that act irreducibly on ℝ2, n
. Apart from SO
0(2, n) itself these are U(1, n/2), SU(1, n/2), if n even, S
1 · SO(1, n/2) if n even and n ≥ 2, and SO
0(1, 2) for n = 3. Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex
hyperbolic space and of the Lie ball. As an application we obtain a list of possible irreducible holonomy groups of Lorentzian
conformal structures, namely SO
0(2, n), SU(1, n), and SO
0(1, 2). 相似文献
12.
Andreas Arvanitoyeorgos Ioannis Chrysikos Yusuke Sakane 《Annals of Global Analysis and Geometry》2010,38(4):413-438
We find the precise number of non-K?hler SO(2n)-invariant Einstein metrics on the generalized flag manifold M = SO(2n)/U(p)×U(n−p) with n ≥ 4 and 2 ≤ p ≤ n−2. We use an analysis on parametric systems of polynomial equations and we give some insight towards the study of such systems.
We also examine the isometric problem for these Einstein metrics. 相似文献
13.
本文首先给出(α,β)-γ开集定义,获得了(α,β)-γ开集性质;然后引入了(α,β)-γ-Ti空间和(α,β)-γ-Ti*空间概念(i=0,1/2,1,2,5/2),并得到它们更广泛的拓扑性质. 相似文献
14.
15.
Let Σ_1 and Σ_2 be m and n dimensional Riemannian manifolds of constant curvature respectively. We assume that w is a unit constant m-form in Σ_1 with respect to which Σ_0 is a graph. We set v = 〈e_1 ∧ … ∧ e_m, 〉), where {e_1, …, e_m} is a normal frame on Σ_t. Suppose that Σ_0 has bounded curvature. If v(x, 0) ≥ v0 > \frac{\sqrt{p}}{2} for all x, then the mean curvature flow has a global solution F under some suitable conditions on the curvatrue of Σ_1 and Σ_2. 相似文献
16.
17.
18.
In the present paper, for a boundary value problem with noncoordinated degeneration of the data and a singularity in the solution,
we show that the R
ν
-generalized solution belongs to the weighted space W
2,ν+gb
2+κ+1/κ+2 (Ω, δ)(κ > 0).
Original Russian Text ? V.A. Rukavishnikov, E.V. Kuznetsova, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45,
No. 6, pp. 894–898. 相似文献
19.
For a bounded system of linear equalities and inequalities, we show that the NP-hard ℓ
0-norm minimization problem is completely equivalent to the concave ℓ
p
-norm minimization problem, for a sufficiently small p. A local solution to the latter problem can be easily obtained by solving a provably finite number of linear programs. Computational
results frequently leading to a global solution of the ℓ
0-minimization problem and often producing sparser solutions than the corresponding ℓ
1-solution are given. A similar approach applies to finding minimal ℓ
0-solutions of linear programs. 相似文献
20.
Samuel A. Ilori 《K-Theory》1989,2(5):623-624
We use the work of Karoubi and Mudrinski on the real Grothendieck's groups of certain complex projective bundles to show that the torsion of the KO
–i
groups of G
3(
n
), n odd, are related to the known torsion of the KO
–i
groups of G2(
n
). 相似文献