共查询到20条相似文献,搜索用时 31 毫秒
1.
Selçuk Demir 《Geometriae Dedicata》2004,105(1):189-207
Let G denote the isometry group of a regular tree of degree ≥3. The notion of congruence subgroup is introduced and finite generation
of the congruence Hecke algebras is proven. Let U be congruence subgroup and
(G; U) be the category of smooth representations of G generated by their U-fixed vectors. We also show that this subcategory is closed under taking subquotients. All these results are analogues of
well-known results in the case of p-adic groups. It is also shown that the category of admissible representation of G is Noetherian in the sense that every subrepresentation of a finitely generated admissible representation is again finitely
generated. Since we want to emphesize the similarities between these groups and p-adic groups, we give the same proofs which also work in the p-adic case whenever possible. 相似文献
2.
Jean-Christophe Bourgoin 《Annals of Global Analysis and Geometry》2007,32(1):1-13
In this paper, we study the minimality of the map for the weighted energy functional , where is a continuous function. We prove that for any integer and any non-negative, non-decreasing continuous function f, the map minimizes E
f,p
among the maps in which coincide with on . The case p = 1 has been already studied in [Bourgoin J.-C. Calc. Var. (to appear)]. Then, we extend results of Hong (see Ann. Inst.
Poincaré Anal. Non-linéaire 17: 35–46 (2000)). Indeed, under the same assumptions for the function f, we prove that in dimension n ≥ 7 for any real with , the map minimizes E
f,p
among the maps in which coincide with on .
相似文献
3.
Elton Pasku 《Semigroup Forum》2008,76(3):427-468
If a monoid S is given by some finite complete presentation ℘, we construct inductively a chain of CW-complexes
such that Δ
n
has dimension n, for every 2≤m≤n, the m-skeleton of Δ
n
is Δ
m
, and p
m
are critical (m+1)-cells with 1≤m≤n−2. For every 2≤m≤n−1, the following is an exact sequence of (ℤS,ℤS)-bimodules
where
if m=2. We then use these sequences to obtain a free finitely generated bimodule partial resolution of ℤS. Also we show that for groups properties FDT and FHT coincide. 相似文献
4.
Darko Zubrinić 《Archiv der Mathematik》2006,87(2):154-162
Assuming that 0 < α p < N, p, q ∈(1,∞), we construct a class of functions in the Besov space
such that the Hausdorff dimension of their singular set is equal to N − α p. We show that these functions are maximally singular, that is, the Hausdorff dimension of the singular set of any other Besov
function in
is ≦ N − α p. Similar results are obtained for Lizorkin-Triebel spaces
and for the Hardy space
. Some open problems are listed.
Received: 5 July 2005; revised: 18 October 2005 相似文献
5.
We study pro-‘finite dimensional finite exponent’ completions of restricted Lie algebras over finite fields of characteristicp. These compact Hausdorff topological restricted Lie algebras, called pro-
restricted Lie algebras, are the restricted Lie-theoretic analogues of pro-p groups. A structure theory for pro-
restricted Lie algebras with finite rank is developed. In particular, the centre of such a Lie algebra is shown to be open.
As an application we examinep-adic analytic pro-p groups in terms of their associated pro-
restricted Lie algebras.
Supported by NSERC of Canada. 相似文献
6.
In this paper, we prove that if a sequence of homeomorphisms , with bounded planar domains, of Sobolev space has uniformly equibounded distortions in EXP(Ω) and weakly converges to f in then the matrices A(x, f
j
) of the corresponding Laplace-Beltrami operators Γ-converge in the Orlicz–Sobolev space , where Q(t) = t
2log(e + t), to the matrix A(x, f) of the Laplace-Beltrami operator associated to f.
相似文献
7.
Davar Khoshnevisan Narn-Rueih Shieh Yimin Xiao 《Probability Theory and Related Fields》2008,140(1-2):129-167
Let X
1, ..., X
N
denote N independent, symmetric Lévy processes on R
d
. The corresponding additive Lévy process is defined as the following N-parameter random field on R
d
:
Khoshnevisan and Xiao (Ann Probab 30(1):62–100, 2002) have found a necessary and sufficient condition for the zero-set of to be non-trivial with positive probability. They also provide bounds for the Hausdorff dimension of which hold with positive probability in the case that can be non-void.
Here we prove that the Hausdorff dimension of is a constant almost surely on the event . Moreover, we derive a formula for the said constant. This portion of our work extends the well known formulas of Horowitz
(Israel J Math 6:176–182, 1968) and Hawkes (J Lond Math Soc 8:517–525, 1974) both of which hold for one-parameter Lévy processes.
More generally, we prove that for every nonrandom Borel set F in (0,∞)
N
, the Hausdorff dimension of is a constant almost surely on the event . This constant is computed explicitly in many cases.
The research of N.-R. S. was supported by a grant from the Taiwan NSC. 相似文献
8.
Kenji Kamizono 《Proceedings of the Steklov Institute of Mathematics》2009,265(1):115-130
In this paper, we generalize the result of Bikulov and Volovich (1997) and construct a p-adic Brownian motion over ℚ
p
. First, we construct directly a p-adic white noise over ℚ
p
by using a specific complete orthonormal system of (ℚ
p
). A p-adic Brownian motion over ℚ
p
is then constructed by the Paley-Wiener method. Finally, we introduce a p-adic random walk and prove a theorem on the approximation of a p-adic Brownian motion by a p-adic random walk. 相似文献
9.
Ken Söze 《Israel Journal of Mathematics》2017,219(2):817-834
We show that for every finitely presented pro-p nilpotent-by-abelian-by-finite group G there is an upper bound on \({\dim _{{\mathbb{Q}_p}}}\left( {{H_1}\left( {M,{\mathbb{Z}_p}} \right){ \otimes _{{\mathbb{Z}_p}}}{\mathbb{Q}_p}} \right)\), as M runs through all pro-p subgroups of finite index in G. 相似文献
10.
We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra
of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators a,b,c,d. We discover a family of automorphisms for which the “twisted” Hochschild dimension coincides with the classical dimension
of
, thus avoiding the “dimension drop” in Hochschild homology seen for many quantum deformations. Strikingly, the simplest such
automorphism is the canonical modular automorphism arising from the Haar functional. In addition, we identify the twisted
cyclic cohomology classes corresponding to the three covariant differential calculi over quantum SU(2) discovered by Woronowicz. 相似文献
11.
We prove that the submodule in K-theory which gives the exact value
of the L-function by the Beilinson regulator map at non-critical values for Hecke characters of imaginary quadratic fields K with cl (K) = 1(p-local Tamagawa number conjecture) satisfies that the length of its coimage under the local Soulé regulator map is the p-adic valuation of certain special values of p-adic L-functions associated to the Hecke characters. This result yields immediately, up to Jannsens conjecture, an upper bound for
in terms of the valuation of these p-adic L-functions, where Vp denotes the p-adic realization of a Hecke motive.Received: 4 June 2003 相似文献
12.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
13.
We define a partition of Z into intervals {I
j} and prove the Littlewood-Paley inequality ‖f‖
p
≦C
p‖Sf‖
p
, 2≦p<∞. Heref is a function on [o, 2π) and
. This is a new example of a partition having the Littlewood-Paley property since the {I
j} are not of the type obtained by iterating lacunary partitions finitely many times. 相似文献
14.
Victor Alexandru Nicolae Popescu Alexandru Zaharescu 《Central European Journal of Mathematics》2008,6(3):351-356
Let p be a prime number, ℚ
p
the field of p-adic numbers, and
a fixed algebraic closure of ℚ
p
. We provide an analytic version of the normal basis theorem which holds for normal extensions of intermediate fields ℚ
p
⊆ K ⊆ L ⊆
.
相似文献
15.
Dirk Segers 《Mathematische Annalen》2006,336(3):659-669
Let K be a p-adic field, R the valuation ring of K, P the maximal ideal of R and q the cardinality of the residue field R/P. Let f be a polynomial over R in n >1 variables and let χ be a character of . Let M
i
(u) be the number of solutions of f = u in (R/P
i
)
n
for and. These numbers are related with Igusa’s p-adic zeta function Z
f,χ(s) of f. We explain the connection between the M
i
(u) and the smallest real part of a pole of Z
f,χ(s). We also prove that M
i
(u) is divisible by , where the corners indicate that we have to round up. This will imply our main result: Z
f,χ(s) has no poles with real part less than − n/2. We will also consider arbitrary K-analytic functions f. 相似文献
16.
I. A. Yurov 《Mathematical Notes》1998,63(6):823-836
Let {a
n
}
n
=0/
be a uniformly distributed sequence ofp-adic integers. In the present paper we study continuous functions close to differentiable ones (with respect to thep-adic metric); for these functions, either the sequence {f(a
n
)}
n
=0/
is uniformly distributed over the ring ofp-adic integers or, for all sufficiently largek, the sequences {f
k
(k(an))}
n
=0/
are uniformly distributed over the residue class ring modp
k
, where
k
is the canonical epimorphism of the ring ofp-adic integers to the residue class ring modp
k
andf
k
is the function induced byf on the residue class ring modp
k
(i.e.,f k
(x)
=f(
k
(x)) (modp
k
)). For instance, these functions can be used to construct generators of pseudorandom numbers.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 935–950, June, 1998.In conclusion, the author wishes to express his deep gratitude to V. S. Anashin for permanent attention to this research and for support. 相似文献
17.
Stanisaw Betley 《K-Theory》2005,36(3-4):291-303
Assume that M is an R-bimodule. Let End(R, M) denotes the category whose objects are pairs (P, f), where P is a finitely generated projective right R-module and f: P → P ⊗ M. It has an exact structure obtained from the category of projectives over R by forgetting f s. We prove that, when R is a field, we have
denotes certain localization of the tensor algebra spanned by M. This result should be viewed as a special case of the noncommutative extension of the results of [4]. 相似文献
18.
Our main result is that the simple Lie group G = Sp(n, 1) acts metrically properly isometrically on L
p
(G) if p > 4n + 2. To prove this, we introduce Property , with V being a Banach space: a locally compact group G has Property if every affine isometric action of G on V, such that the linear part is a C
0-representation of G, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic
groups over a local field of characteristic zero, have Property . As a consequence, for unitary representations, we characterize those groups in the latter classes for which the first cohomology
with respect to the left regular representation on L
2(G) is nonzero; and we characterize uniform lattices in those groups for which the first L2-Betti number is nonzero.
相似文献
19.
P. E. Bradley 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(2):118-127
In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to
p-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions
of ℚ
p
and discuss p-adic DNA encoding. The application leads to fast p-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint
of p-adic geometry, to encode a dendrogram X in a p-adic field K means to fix a set S of K-rational punctures on the p-adic projective line ℙ1. To ℙ1 \ S is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers X, a method first used by F. Kato in 1999 in the classification of discrete subgroups of PGL2(K). Next, we show how the p-adic moduli space of ℙ1 with n punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions
on ℙ1. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a p-adic algebraic curve with totally degenerate reduction modulo p. Finally, we indicate some of our results in the study of general discrete actions on ℙ1, and their relation to p-adic Hurwitz spaces.
The text was submitted by the author in English. 相似文献
20.
S. G. Kolesnikov 《Journal of Mathematical Sciences》2008,152(2):220-246
In this paper, we prove that any automorphism of a Sylow p-subgroup of the Chevalley group over the ring
(where p is prime and m ≥ 1) is a product of graph, inner, diagonal, and hypercentral automorphisms.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 8, pp. 121–158, 2006. 相似文献