首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
It is shown that, if is an isomorphism between semisimple weightedmeasure algebras M(w1) and M(w2), then maps L1(R+, w1) ontoL1(R+, w2). This is used to describe all the automorphisms ofM(R+, w). A necessary and sufficient condition is given forM(w1) and M(w2) to be isomorphic.  相似文献   

2.
This article introduces the notion of 2-ruled 4-folds: submanifoldsof Rn fibred over a 2-fold by affine 2-planes. This is motivatedby a paper by Joyce and previous work of the present author.A 2-ruled 4-fold M is r-framed if an oriented basis is smoothlyassigned to each fibre, and then we may write M in terms oforthogonal smooth maps 1,2 : Sn–1 and a smooth map : Rn. We focus on 2-ruled Cayley 4-folds in R8 as certainother calibrated 4-folds in R7 and R8 can be considered as specialcases. The main result characterizes non-planar, r-framed, 2-ruledCayley 4-folds, using a coupled system of nonlinear, first-order,partial differential equations that 1 and 2 satisfy, and anothersuch equation on which is linear in . We give a means of constructing2-ruled Cayley 4-folds starting from particular 2-ruled Cayleycones using holomorphic vector fields. This is used to giveexplicit examples of U(1)-invariant 2-ruled Cayley 4-folds asymptoticto a U(1)3-invariant 2-ruled Cayley cone. Examples are alsogiven based on ruled calibrated 3-folds in C3 and R7 and complexcones in C4.  相似文献   

3.
By critical point theory, a new approach is provided to studythe existence of periodic and subharmonic solutions of the secondorder difference equation where f C(R x Rm, Rm), f(t+M,z)+f(t,z) for any (t, z)R x Rmand M is a positive integer. This is probably the first timecritical point theory has been applied to deal with the existenceof periodic solutions of difference systems.  相似文献   

4.
Let MS be the universal maximal operator over unit vectors ofarbitrary directions. This operator is not bounded in L2(R2).We consider a sequence of operators over sets of finite equidistributeddirections converging to MS. We provide a new proof of N. Katz'sbound for such operators. As a corollary, we deduce that MSis bounded from some subsets of L2 to L2. These subsets arecomposed of positive functions whose Fourier transforms havea logarithmic decay or which are supported on a disc. 1991 MathematicsSubject Classification 42B25.  相似文献   

5.
This paper provides a proof that an n-dimensional complete openRiemannian manifold M with sectional curvature KM –1is diffeomorphic to a Euclidean n-space Rn if the volume growthof geodesic balls in M is close to that of the balls in an n-dimensionalhyperbolic space Hn(–1) of sectional curvature –1.  相似文献   

6.
Spaces of Harmonic Functions   总被引:1,自引:0,他引:1  
It is important and interesting to study harmonic functionson a Riemannian manifold. In an earlier work of Li and Tam [21]it was demonstrated that the dimensions of various spaces ofbounded and positive harmonic functions are closely relatedto the number of ends of a manifold. For the linear space consistingof all harmonic functions of polynomial growth of degree atmost d on a complete Riemannian manifold Mn of dimension n,denoted by Hd(Mn), it was proved by Li and Tam [20] that thedimension of the space H1(M) always satisfies dimH1(M) dimH1(Rn)when M has non-negative Ricci curvature. They went on to askas a refinement of a conjecture of Yau [32] whether in generaldim Hd(Mn) dimHd(Rn)for all d. Colding and Minicozzi made animportant contribution to this question in a sequence of papers[5–11] by showing among other things that dimHd(M) isfinite when M has non-negative Ricci curvature. On the otherhand, in a very remarkable paper [16], Li produced an elegantand powerful argument to prove the following. Recall that Msatisfies a weak volume growth condition if, for some constantA and , (1.1) for all x M and r R, where Vx(r) is the volume of the geodesicball Bx(r) in M; M has mean value property if there exists aconstant B such that, for any non-negative subharmonic functionf on M, (1.2) for all p M and r > 0.  相似文献   

7.
A straightforward implementation of the Global Element Method(Delves & Hall, 1979) for two-dimensional partial differentialequations has an operation count: Set up equations: (MN6); solve: (M3N6) where M is the number of elements and N the number of one-dimensionalexpansion functions used in each element. We describe here analternative implementation in which both of these counts arereduced to (MN4). The method used generalizes to p dimensions, with operationcount (MN2p) compared with the "standard" count (MP3p + M3N3p).  相似文献   

8.
An n-affine manifold is a differentiable manifold endowed withan atlas whose transition functions are locally affine transformationsof Rn. The paper studies affine dynamic, that is, affine endomorphismsof affine manifolds. The main goal is to relate the dynamicalviewpoint to the completeness problem. In particular, it isshown that the Markus conjecture is true when dim Aff(M, ) >dim M – 2.  相似文献   

9.
We prove that any (real or complex) analytic horizontally conformalsubmersion from a three-dimensional conformal manifold (M3,cM) to a two-dimensional conformal manifold (N2, cN) can be,locally, ‘extended’ to a unique harmonic morphismfrom the (eaven)-space (H4, g) of (M3, cN) to (N2, cN). Moreover,any positive harmonic morphism with two-dimensional fibres from(H4, g) is obtained in this way.  相似文献   

10.
A simple two-dimensional model is used to demonstrate some interestingeffects which arise when Chandrasekhar's (1962) theory of overstableconvection in an infinite rotating fluid layer is modified totake account of lateral walls. The aim of the investigationis to determine how sidewalls aligned with the convective rollsaffect the critical Rayleigh number and frequency of oscillationand also how the overstable eigensolutions are related to thepreviously determined stationary solutions of the equations(Daniels, 1977). For containers of large aspect ratio, L, thecritical Rayleigh number for overstability is Ro+O(L–1)(where Ro is the value for the infinite layer) and in the neighbourhoodof this single perturbed value it is found that there is aninfinite spectrum of overstable eigenvalues with frequencieswhich differ by O(L–1). The O(L–1) correction toRo is determined analytically for the case of small Prandtlnumber and rapid rotation.  相似文献   

11.
This paper presents a rigidity theorem for infinite-dimensionalBergman spaces of hyperbolic Riemann surfaces, which statesthat the Bergman space A1(M), for such a Riemann surface M,is isomorphic to the Banach space of summable sequence, l1.This implies that whenever M and N are Riemann surfaces thatare not analytically finite, and in particular are not necessarilyhomeomorphic, then A1(M) is isomorphic to A1(N). It is knownfrom V. Markovic that if there is a linear isometry betweenA1(M) and A1(N), for two Riemann surfaces M and N of non-exceptionaltype, then this isometry is induced by a conformal mapping betweenM and N. As a corollary to this rigidity theorem presented here,taking the Banach duals of A1(M) and l1 shows that the spaceof holomorphic quadratic differentials on M, Q(M), is isomorphicto the Banach space of bounded sequences, l. As a consequenceof this theorem and the Bers embedding, the Teichmüllerspaces of such Riemann surfaces are locally bi-Lipschitz equivalent.  相似文献   

12.
S. A. Sauter Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland Many important physical applications are governed by the waveequation. The formulation as time domain boundary integral equationsinvolves retarded potentials. For the numerical solution ofthis problem, we employ the convolution quadrature method forthe discretization in time and the Galerkin boundary elementmethod for the space discretization. We introduce a simple apriori cut-off strategy where small entries of the system matricesare replaced by zero. The threshold for the cut-off is determinedby an a priori analysis which will be developed in this paper.This analysis will also allow to estimate the effect of additionalperturbations such as panel clustering and numerical integrationon the overall discretization error. This method reduces thestorage complexity for time domain integral equations from O(M2N)to O(M2N logM), where N denotes the number of time steps andM is the dimension of the boundary element space.  相似文献   

13.
Let (R,m) be a local ring with prime ideals p and q such that. If R is regular and containsa field, and dim(R/p)+dim(R/q)=dim(R), then it is proved thatp(m) q(n) mm+n for all positive integers m and n. This isproved using a generalization of Serre's Intersection Theoremwhich is applied to a hypersurface R/fR. The generalizationgives conditions that guarantee that Serre's bound on the intersectiondimension (R/p)+(R/q)dim(R) holds when R is nonregular.  相似文献   

14.
We exhibit closed manifolds M covered by S2n–1 x Rk forall n 2 and for sufficiently large k, with fundamental groupsof infinite virtual cohomological dimension. These examplesare based on results of Raghunathan on lattices in covers ofspin and symplectic groups, and address a problem first raisedby Wall.  相似文献   

15.
Using the BMO-H1 duality (among other things), D. R. Adams provedin [1] the strong type inequality whereC is some positive constant independent of f. Here M is theHardy–Littlewood maximal operator in Rn, H is the -dimensionalHausdorff content, and the integrals are taken in the Choquetsense. The Choquet integral of 0 with respect to a set functionC is defined by Precise definitionsof M and H will be given below. For an application of (1) tothe Sobolev space W1, 1 (Rn), see [1, p. 114]. The purpose of this note is to provide a self-contained, directproof of a result more general than (1). 1991 Mathematics SubjectClassification 28A12, 28A25, 42B25.  相似文献   

16.
Thompson's famous theorems on singular values–diagonalelements of the orbit of an nxn matrix A under the action (1)U(n) U(n) where A is complex, (2) SO(n) SO(n), where A isreal, (3) O(n) O(n) where A is real are fully examined. Coupledwith Kostant's result, the real semi-simple Lie algebra son,n yields (2) and hence (3) and the sufficient part (the hardpart) of (1). In other words, the curious subtracted term(s)are well explained. Although the diagonal elements correspondingto (1) do not form a convex set in Cn, the projection of thediagonal elements into Rn (or iRn) is convex and the characterizationof the projection is related to weak majorization. An elementaryproof is given for this hidden convexity result. Equivalentstatements in terms of the Hadamard product are also given.The real simple Lie algebra sun, n shows that such a convexityresult fits into the framework of Kostant's result. Convexityproperties and torus relations are studied. Thompson's resultson the convex hull of matrices (complex or real) with prescribedsingular values, as well as Hermitian matrices (real symmetricmatrices) with prescribed eigenvalues, are generalized in thecontext of Lie theory. Also considered are the real simple Liealgebras sop, q and sop, q, p < q, which yield the rectangularcases. It is proved that the real part and the imaginary partof the diagonal elements of complex symmetric matrices withprescribed singular values are identical to a convex set inRn and the characterization is related to weak majorization.The convex hull of complex symmetric matrices and the convexhull of complex skew symmetric matrices with prescribed singularvalues are given. Some questions are asked.  相似文献   

17.
We propose an algorithm which for any real number r, any k ?l matrix M and any k-vector y, finds the l-vector x which minimizes||x||2r2||Mxy||2, i.e. it finds the "regularized"solution to the equation Mx = y. (|| || denotes the 2-norm.)The algorithm is iterative with the following properties: (i)in a single step it needs access to only one row of the matrixM, (ii) it needs to store only the present estimate of the solution(size l) and a "residual vector" of size k, (iii) in a singlestep it updates only one component of the residual vector. Becauseof these properties the algorithm has been found useful in "solving"very large inconsistent systems of equations. Convergence ofthe algorithm to the desired solution is proved and the rateof convergence of the algorithm is illustrated. The algorithmis considered here, not because it is believed to be generallysuperior to more commonly used iterative methods, but becausefor certain very large problems it may be the only feasiblemethod from the point of view of storage requirements.  相似文献   

18.
Let M be a manifold with conical ends. (For precise definitionssee the next section; we only mention here that the cross-sectionK can have a nonempty boundary.) We study the scattering forthe Laplace operator on M. The first question that we are interestedin is the structure of the absolute scattering matrix S(s).If M is a compact perturbation of Rn, then it is well-knownthat S(s) is a smooth perturbation of the antipodal map on asphere, that is, S(s)f(·)=f(–·) (mod C) On the other hand, if M is a manifold with a scattering metric(see [8] for the exact definition), it has been proved in [9]that S(s) is a Fourier integral operator on K, of order 0, associatedto the canonical diffeomorphism given by the geodesic flow atdistance . In our case it is possible to prove that S(s) isin fact equal to the wave operator at a time t = plus C terms.See Theorem 3.1 for the precise formulation. This result isnot too difficult and is obtained using only the separationof variables and the asymptotics of the Bessel functions. Our second result is deeper and concerns the scattering phasep(s) (the logarithm of the determinant of the (relative) scatteringmatrix).  相似文献   

19.
Address from 1st April 1985, School of Mathematics, Universityof Bristol, University Walk, Bristol BS8 1TW. The morning finite-element method for evolutionary partial differentialequations leads to a coupled non-linear system of ordinary differentialequations in time, with a coefficien matrix A, say, for thetime derivaties, We show for linear elements in any number ofdimensions, A can be written in the form MTCM, where the matrixC depends solely on the mesh geometry and the matrix M on thegradient of the section, As a simple consequence we show thatA is singular only in the cases (i) element degeneracy () and (ii) collinearity of nodes (M not out of fullrank). We give constructions for the inversion of A in all cases. In one dimension, if A is non-singular, it has a simple explicitinverse. If A is singular we replace it by reduced matrix A*.It can be shown that every case the spectral radius of the Jacobiiteration matrix ia ?and that A or A* can be efficiently invertedby conjugate gradient methods. Finally, we discuss the applicability of these arguments tosystem of equations in any number of dimensions.  相似文献   

20.
It is proved here that a minimal isometric immersion of a Kähler-Einsteinor homogeneous Kähler-manifold into an Euclidean spacemust be totally geodesic. As an application, it is shown thatan open subset of the real hyperbolic plane RH2 cannot be minimallyimmersed into the Euclidean space. As another application, aproof is given that if an irreducible Kähler manifold isminimally immersed in a Euclidean space, then its restrictedholonomy group must be U(n), where n = dimCM. 2000 MathematicsSubject Classification 53B25 (primary); 53C42 (secondary).  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号