共查询到20条相似文献,搜索用时 125 毫秒
1.
Throughout this paper G(k) denotes a Chevalley group of rankn defined over the field k, where n3. Let be the root systemassociated with G(k) and let ={1, 2, ..., n} be a set of fundamentalroots of , with + being the set of positive roots of with respectto . For and +, let n() be the coefficient of in the expressionof as a sum of fundamental roots; so =n(). Also we recall thatht(), the height of , is given by ht()=n(). The highest rootin + will be denoted by . We additionally assume that the Dynkindiagram of G(k) is connected. 相似文献
2.
Consider the following infinite dimensional stochastic evolutionequation over some Hilbert space H with norm |·|:
It is proved that under certain mild assumptions, the strongsolution Xt(x0)VHV*, t 0, is mean square exponentially stableif and only if there exists a Lyapunov functional (·,·):HxR+R1 which satisfies the following conditions: (i)c1|x|2k1eµ1t(x,t)c2|x|2+k2+k2eµ2t; (ii) L(x,t)c3(x,t)+k3eµ3t, xV, t0; where L is the infinitesimal generator of the Markov processXt and ci, ki, µi, i = 1, 2, 3, are positive constants.As a by-product, the characterization of exponential ultimateboundedness of the strong solution is established as the nulldecay rates (that is, µi = 0) are considered. 相似文献
3.
Haller-Dintelmann Robert; Heck Horst; Hieber Matthias 《Journal London Mathematical Society》2006,74(3):717-736
Consider a parabolic NxN-system of order m on n with top-ordercoefficients a VMOL. Let 1 < p, q < and let be a Muckenhouptweight. It is proved that systems of this kind possess a uniquesolution u satisfying
whereAu = ||m a Du and J = [0,). In particular, choosing = 1, therealization of A in Lp(n)N has maximal Lp – Lq regularity. 相似文献
4.
Let G be a permutation group on a set , and let m and k be integerswhere 0<m<k. For a subset of , if the cardinalities ofthe sets g\, for gG, are finite and bounded, then is said tohave bounded movement, and the movement of is defined as move()=maxgG|g\|. If there is a k-element subset such that move()m, it is shown that some G-orbit has length at most (k2m)/(km).When combined with a result of P. M. Neumann, this result hasthe following consequence: if some infinite subset has boundedmovement at most m, then either is a G-invariant subset withat most m points added or removed, or nontrivially meets aG-orbit of length at most m2+m+1. Also, if move ()m for allk-element subsets and if G has no fixed points in , then either||k+m (and in this case all permutation groups on have thisproperty), or ||5m2. These results generalise earlierresults about the separation of finite sets under group actionsby B. J. Birch, R. G. Burns, S. O. Macdonald and P. M. Neumann,and groups in which all subsets have bounded movement (by theauthor). 相似文献
5.
Let G be a separable locally compact group and let be its dualspace with Fell's topology. It is well known that the set P(G)of continuous positive-definite functions on G can be identifiedwith the set of positive linear functionals on the group C*-algebraC*(G). We show that if is discrete in , then there exists anonzero positive-definite function associated with such that is a w*-strongly exposed point of P(G)0, where P(G)0={f P(G):f(e)1. Conversely, if some nonzero positive-definite function associatedwith is a w*-strongly exposed point of P(G)0, then is isolatedin . Consequently, G is compact if and only if, for every ,there exists a nonzero positive-definite function associatedwith that is a w*-strongly exposed point of P(G)0. If, in addition,G is unimodular and , then is isolated in if and only if somenonzero positive-definite function associated with is a w*-stronglyexposed point of P(G)0, where is the left regular representationof G and is the reduced dual space of G. We prove that if B(G)has the RadonNikodym property, then the set of isolatedpoints of (so square-integrable if G is unimodular) is densein . It is also proved that if G is a separable SIN-group, thenG is amenable if and only if there exists a closed point in. In particular, for a countable discrete non-amenable groupG (for example the free group F2 on two generators), there isno closed point in its reduced dual space . 相似文献
6.
Buff Xavier; Fagella NuRia; Geyer Lukas; Henriksen Christian 《Journal London Mathematical Society》2005,72(3):689-716
For (,a) C* x C, let f,a be the rational map defined by f,a(z)= z2 (az+1)/(z+a). If R/Z is a Brjuno number, we let D bethe set of parameters (,a) such that f,a has a fixed Hermanring with rotation number (we consider that (e2i,0) D). Resultsobtained by McMullen and Sullivan imply that, for any g D, theconnected component of D(C* x (C/{0,1})) that contains g isisomorphic to a punctured disk. We show that there is a holomorphic injection F:DD such thatF(0) = (e2i ,0) and , where r is the conformal radius at 0 of the Siegel disk of the quadraticpolynomial z e2i z(1+z). As a consequence, we show that for a (0,1/3), if fl,a has afixed Herman ring with rotation number and if ma is the modulusof the Herman ring, then, as a0, we have e ma=(r/a) + O(a). We finally explain how to adapt the results to the complex standardfamily z e(a/2)(z-1/z). 相似文献
7.
Let =(n)n1 be a log concave sequence such that lim infn+n/nc>0for some c>0 and ((log n)/n)n1 is nonincreasing for some<1/2. We show that, if T is a contraction on the Hilbertspace with spectrum a Carleson set, and if ||Tn||=O(n)as n tends to + with n11/(n log n)=+, then T is unitary. Onthe other hand, if n11/(n log n)<+, then there exists a (non-unitary)contraction T on the Hilbert space such that the spectrum ofT is a Carleson set, ||Tn||=O(n) as n tends to +, andlim supn+||Tn||=+. 相似文献
8.
In this paper we continue our investigation in [5, 7, 8] onmultipeak solutions to the problem 2u+u=Q(x)|u|q2u, xRN, uH1(RN) (1.1) where = Ni=12/x2i is the Laplace operator in RN, 2 < q < for N = 1, 2, 2 < q < 2N/(N2) for N3, and Q(x)is a bounded positive continuous function on RN satisfying thefollowing conditions. (Q1) Q has a strict local minimum at some point x0RN, that is,for some > 0 Q(x)>Q(x0) for all 0 < |xx0| < . (Q2) There are constants C, > 0 such that |Q(x)Q(y)|C|xy| for all |xx0| , |yy0| . Our aim here is to show that corresponding to each strict localminimum point x0 of Q(x) in RN, and for each positive integerk, (1.1) has a positive solution with k-peaks concentratingnear x0, provided is sufficiently small, that is, a solutionwith k-maximum points converging to x0, while vanishing as 0 everywhere else in RN. 相似文献
9.
The paper considers finite subsets Zd which possess the extensionproperty, namely that every collection {ck}k of complexnumbers which is positive definite with respect to is the restrictionof the Fourier coefficients of some positive measure on Td.All finite subsets of Z2 which possess the extension propertyare described. 相似文献
10.
Suppose that X1, X2, X3, ... are independent random points inRd with common density f, having compact support with smoothboundary , with f| continuous. Let Rni, k denote the distancefrom Xi to its kth nearest neighbour amongst the first n points,and let Mn, k = maxin Rni, k. Let denote the volume of theunit ball. Then as n ,
, almost surely If instead the points lie in a compact smooth d-dimensionalRiemannian manifold K, then nMdn, k/log n (minKf)1,almost surely. 相似文献
11.
If = {1, 2, ..., s}, where 1 2 ... s > 0, is a partitionof n then denotes the associated irreducible character of Sn,the symmetric group on {1, 2, ..., n}, and, if cCSn, the groupalgebra generated by C and Sn, then dc(·) denotes thegeneralized matrix function associated with c. If c1, c2 CSnthen we write c1 c2 in case (A) (A) for each n x n positivesemi-definite Hermitian matrix A. If cCSn and c(e) 0, wheree denotes the identity in Sn, then or denotes (c(e))–1 c. The main result, an estimate for the norms of tensors of a certainanti-symmetry type, implies that if = {1, 2, ..., s, 1t} isa partition of n such that s > 1 and s = 2, and ' denotes{1, 2, ..., s-1, 1t} then (, {2}) where denotes characterinduction from Sn–2 x S2 to Sn. This in turn implies thatif = {1, 2, ..., s, 1t} with s > 1, s = 2, and ßdenotes {1 + 2, 2, ..., s-1, 1t} then ß which,in conjunction with other known results, provides many new inequalitiesamong immanants. In particular it implies that the permanentfunction dominates all normalized immanants whose associatedpartitions are of rank 2, a result which has proved elusivefor some years. We also consider the non-relationship problem for immanants– that is the problem of identifying pairs, (,ß)such that ß and ß are both false. 相似文献
12.
Let G be a permutation group on a finite set . A sequence B=(1,..., b) of points in is called a base if its pointwise stabilizerin G is the identity. Bases are of fundamental importance incomputational algorithms for permutation groups. For both practicaland theoretical reasons, one is interested in the minimal basesize for (G, ), For a nonredundant base B, the elementary inequality2|B||G||||B| holds; in particular, |B|log|G|/log||. In the casewhen G is primitive on , Pyber [8, p. 207] has conjectured thatthe minimal base size is less than Clog|G|/log|| for some (large)universal constant C. It appears that the hardest case of Pyber's conjecture is thatof primitive affine groups. Let H=GV be a primitive affine group;here the point stabilizer G acts faithfully and irreduciblyon the elementary abelian regular normal subgroup V of H, andwe may assume that =V. For positive integers m, let mV denotethe direct sum of m copies of V. If (v1, ..., vm)mV belongsto a regular G-orbit, then (0, v1, ..., vm) is a base for theprimitive affine group H. Conversely, a base (1, ..., b) forH which contains 0V= gives rise to a regular G-orbit on (b1)V. Thus Pyber's conjecture for affine groups can be viewed asa regular orbit problem for G-modules, and it is therefore aspecial case of an important problem in group representationtheory. For a related result on regular orbits for quasisimplegroups, see [4, Theorem 6]. 相似文献
13.
The positive cone of the K0-group of the non-commutative sphereB is explicitly determined by means of the four basic unboundedtrace functionals discovered by Bratteli, Elliott, Evans andKishimoto. The C*-algebra B is the crossed product A x Z2 ofthe irrational rotation algebra A by the flip automorphism defined on the canonical unitary generators U, V by (U) = U*,(V) = V*, where VU = e2i UV and is an irrational real number.This result combined with Rieffel's cancellation techniquesis used to show that cancellation holds for all finitely generatedprojective modules over B. Subsequently, these modules are determinedup to isomorphism as finite direct sums of basic modules. Italso follows that two projections p and q in a matrix algebraover B are unitarily equivalent if, and only if, their vectortraces are equal: [p] = [q]. These results will have the following ramifications. They areused (elsewhere) to show that the flip automorphism on A isan inductive limit automorphism with respect to the basic buildingblock construction of Elliott and Evans for the irrational rotationalgebra. This will, in turn, yield a two-tower proof of thefact that B is approximately finite dimensional, first provedby Bratteli and Kishimoto. 相似文献
14.
The close relationship between the notions of positive formsand representations for a C*-algebra A is one of the most basicfacts in the subject. In particular the weak containment ofrepresentations is well understood in terms of positive forms:given a representation of A in a Hilbert space H and a positiveform on A, its associated representation is weakly containedin (that is, ker ker ) if and only if belongs to the weak*closure of the cone of all finite sums of coefficients of .Among the results on the subject, let us recall the followingones. Suppose that A is concretely represented in H. Then everypositive form on A is the weak* limit of forms of the typex ki=1 i, xi with the i in H; moreover if A is a von Neumannsubalgebra of (H) and is normal, there exists a sequence (i)i 1 in H such that (x) = i 1 i, xi for all x. 相似文献
15.
We say that a bounded linear operator T acting on a Banach spaceB is antisupercyclic if for any x B either Tnx = 0 for somepositive integer n or the sequence {Tnx/||Tnx||} weakly convergesto zero in B. Antisupercyclicity of T means that the angle criterionof supercyclicity is not satisfied for T in the strongest possibleway. Normal antisupercyclic operators and antisupercyclic bilateralweighted shifts are characterized. As for the Volterra operator V, it is proved that if 1 p and any f Lp [0,1] then the limit limn (n!||Vnf||p)1/n doesexist and equals 1 inf supp (f). Upon using this asymptoticformula it is proved that the operator V acting on the Banachspace Lp[0,1] is antisupercyclic for any p (1,). The same statementfor p = 1 or p = is false. The analogous results are provedfor operators when the real part of z C is positive. 相似文献
16.
Hayashi Nakao; Kaikina Elena I.; Naumkin Pavel I. 《Journal London Mathematical Society》2005,72(3):663-688
The Cauchy problem is studied for the nonlinear equations withfractional power of the negative Laplacian
where (0,2), with critical = /n and sub-critical (0,/n)powers of the nonlinearity. Let u0 L1,a L C, u0(x) 0 in Rn, = . The case of not small initial data is of interest. It is proved that the Cauchy problemhas a unique global solution u C([0,); L L1,a C) and the largetime asymptotics are obtained. 相似文献
17.
Let K be the field of real or complex numbers. Let (X K2n,) be a symplectic vector space and take 0 < k < n,N =. Let L1,...,LN X be 2k-dimensionallinear subspaces which are in a sufficiently general position.It is shown that if F : X X is a linear automorphism whichpreserves the form k on all subspaces L1,...,LN, then F is ank-symplectomorphism (that is, F* = k, where ). In particular, if K = R and k is odd then F mustbe a symplectomorphism. The unitary version of this theoremis proved as well. It is also observed that the set Al,2r ofall l-dimensional linear subspaces on which the form has rank 2r is linear in the Grassmannian G(l,2n), that is, there isa linear subspace L such that Al,2r = L G(l, 2n). In particular,the set Al,2r can be computed effectively. Finally, the notionof symplectic volume is introduced and it is proved that itis another strong invariant. 相似文献
18.
We study concentration phenomena for the system
in the unit ball B1 of 3 with Dirichlet boundaryconditions. Here , , > 0 and p > 1. We prove the existenceof positive radial solutions (, ) such that concentrates ata distance (/2)|log | away from the boundary B1 as the parameter tends to 0. The approach is based on a combination of LyapunovSchmidtreduction procedure together with a variational method. 相似文献
19.
Spatial concavity properties of non-negative weak solutionsof the filtration equations with absorption ut = ((u))xx(u)in Q = Rx(0, ), '0, 0 are studied. Under certain assumptionson the coefficients , it is proved that concavity of the pressurefunction is a consequence of a weak convexityof travelling-wave solutions of the form V(x, t) = (xt+a).It is established that the global structure of a so-called properset B = {V} of such particular solutions determines a propertyof B-concavity for more general solutions which is preservedin time. For the filtration equation ut = ((u))xx a semiconcavityestimate for the pressure, vxx(t+)1'(), due to the B-concavityof the solution to the subset B of the explicit self-similarsolutions (x/t+)) is proved. The analysis is based on the intersection comparison based onthe Sturmian argument of the general solution u(x, t) with subsetsB of particular solutions. Also studied are other aspects ofthe B-concavity/convexity with respect to different subsetsof explicit solutions. 相似文献
20.
Dilworth S. J.; Ferenczi V.; Kutzarova Denka; Odell E. 《Journal London Mathematical Society》2007,75(2):409-419
Let 1 p and let X be a Banach space with a semi-normalizedstrongly asymptotic p basis (ei). If X is minimal and 1 p <2, then X is isomorphic to a subspace of p. If X is minimaland 2 p < , or if X is complementably minimal and 1 p , then (ei) is equivalent to the unit vector basis of p (orc0 if p = ). 相似文献