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1.
We consider Hilbert transforms along curves on the Heisenberggroup. In particular, necessary and sufficient conditions forthe L2-boundedness are given for (t)=(t,(t),0) when is evenor odd and convex on R+. 1991 Mathematics Subject Classification:42B20, 42B25. 相似文献
2.
The main part of the paper deals with local existence and globalexistence versus blow-up for solutions of the Laplace equationin bounded domains with a non-linear dynamical boundary condition.More precisely, we study the problem consisting in: (1) theLaplace equation in (0, ) x ; (2) a homogeneous Dirichlet condition(0, ) x 0; (3) the dynamical boundary condition ; (4) the initial condition u(0, x) = u0 (x) on . Here is a regular and bounded domain in Rn, with n 1, and0 and 1 endow a measurable partition of . Moreover, m>1,2 p < r, where r = 2 (n 1) / (n 2) whenn 3, r = when n = 1,2, and u0 H1/2 , u0 = 0 on 0. The final part of the paper deals with a refinement of a globalnon-existence result by Levine, Park and Serrin, which is appliedto the previous problem. 2000 Mathematics Subject Classification35K55 (primary), 35K90, 35K77 (secondary). 相似文献
3.
We investigate asphericity of the relative group presentation G,t |atbtctdtet=1 and prove it aspherical provided thesubgroupof G generated by ab1, bc1, cd1, de1is neither finite cyclic nor a finite triangle group. We alsoprove a similar result for the closely related relative grouppresentation G,s,t | sßst=1=tts1. 2000 MathematicsSubject Classification: 20F05, 57M05. 相似文献
4.
We prove that the Novikov assembly map for a group factorizes,in low homological degree, through the algebraicK-theory of its integral group ring. In homological degree 2,this answers a question posed by N. Higson and P. Julg. As adirect application, we prove that if is torsion-free and satisfiesthe Baum-Connes conjecture, then the homology group H1(; Z)injects in and in , for any ring A such that . If moreover B is of dimension lessthan or equal to 4, then we show that H2(; Z) injects in and in , where A is as before, and 2 is generated by the Steinberg symbols{,}, for . 2000 Mathematical Subject Classification: primary 19D55, 19Kxx,58J22; secondary: 19Cxx, 19D45, 43A20, 46L85. 相似文献
5.
The Hardy operator Ta on a tree is defined by Properties of Ta as a map from Lp() into itselfare established for 1 p . The main result is that, with appropriateassumptions on u and v, the approximation numbers an(Ta) ofTa satisfy for a specified constant p and 1 p < . This extends results of Naimark, Newmanand Solomyak for p = 2. Hitherto, for p 2, (*) was unknowneven when is an interval. Also, upper and lower estimates forthe lq and weak-lq norms of an(Ta) are determined. 2000 MathematicalSubject Classification: 47G10, 47B10. 相似文献
6.
We consider a Hamiltonian setup M, , H, L, , P, where M, isa symplectic manifold, L is a distribution of Lagrangian subspacesin M, P is a Lagrangian submanifold of M, H is a smooth time-dependentHamiltonian function on M, and :[a,b] M is an integral curveof the Hamiltonian flow starting at P. We do not require any convexity property of the Hamiltonianfunction H. Under the assumption that (b) is not P-focal, weintroduce the Maslov index imaslov of given in terms of thefirst relative homology group of the Lagrangian Grassmannian;under generic circumstances imaslov() is computed as a sortof algebraic count of the P-focal points along . We prove thefollowing version of the Index Theorem: under suitable hypotheses,the Morse index of the Lagrangian action functional restrictedto suitable variations of is equal to the sum of imaslov()and a convexity term of the Hamiltonian H relative to the submanifoldP. When the result is applied to the case of the cotangent bundleM = TM* of a semi-Riemannian manifold (M, g) and to the geodesicHamiltonian , we obtain a semi-Riemannian version of the celebrated Morse Index Theorem for geodesicswith variable endpoints in Riemannian geometry. 2000 MathematicalSubject Classification: 37J05, 53C22, 53C50, 53D12, 70H05. 相似文献
7.
By a Kleinian group we mean a discrete subgroup of PSL(2, C).We prove that abelian subgroups of finitely generated Kleiniangroups are separable. In other words, if M = H3/ is a hyperbolic3-orbifold, with finitely generated, then abelian subgroupsof are separable in . 1991 Mathematics Subject Classification20E26, 51M10, 57M05. 相似文献
8.
We consider the stationary non-linear Schrödinger equation where > 0 and the functionsf and g are such that and for some bounded open set RN. We use topological methods to establish the existenceof two connected sets D± of positive/negative solutionsin R x W2, p RN where that cover the interval (, ()) in the sense that
and furthermore,
The number () is characterized as the unique value of in theinterval (, ) for which the asymptotic linearization has a positiveeigenfunction. Our work uses a degree for Fredholm maps of indexzero. 2000 Mathematics Subject Classification 35J60, 35B32,58J55. 相似文献
9.
Let F:Cn Cn be a holomorphic map, Fk be the kth iterate ofF, and p Cn be a periodic point of F of period k. That is,Fk(p) = p, but for any positive integer j with j < k, Fj(p) p. If p is hyperbolic, namely if DFk(p) has no eigenvalue ofmodulus 1, then it is well known that the dynamical behaviourof F is stable near the periodic orbit = {p, F(p),..., Fk1(p)}.But if is not hyperbolic, the dynamical behaviour of F near may be very complicated and unstable. In this case, a veryinteresting bifurcational phenomenon may occur even though may be the only periodic orbit in some neighbourhood of : forgiven M N\{1}, there may exist a Cr-arc {Ft: t [0,1]} (wherer N or r = ) in the space H(Cn) of holomorphic maps from Cninto Cn, such that F0 = F and, for t (0,1], Ft has an Mk-periodicorbit t with as t 0. Theperiod thus increases by a factor M under a Cr-small perturbation!If such an Ft does exist, then , as well as p, is said to beM-tupling bifurcational. This definition is independent of r. For the above F, there may exist a Cr-arc in H(Cn), with t [0,1], such that and, for t (0,1], has two distinct k-periodic orbits t,1 and t,2 with d(t,i, ) 0 as t 0 for i = 1,2. If such an does exist, then , as well as p, is said to be 1-tupling bifurcational. In recent decades, there have been many papers and remarkableresults which deal with period doubling bifurcations of periodicorbits of parametrized maps. L. Block and D. Hart pointed outthat period M-tupling bifurcations cannot occur for M >2 in the 1-dimensional case. There are examples showing thatfor any M N, period M-tupling bifurcations can occur in higher-dimensionalcases. An M-tupling bifurcational periodic orbit as defined here actsas a critical orbit which leads to period M-tupling bifurcationsin some parametrized maps. The main result of this paper isthe following. Theorem. Let k N and M N, and let F: C2 C2 be a holomorphicmap with k-periodic point p. Then p is M-tupling bifurcationalif and only if DFk(p) has a non-zero periodic point of periodM. 1991 Mathematics Subject Classification: 32H50, 58F14. 相似文献
10.
Let , :N N be morphisms of degree at least 2 whose canonicalheights and are identical. We draw various conclusions aboutthe Green functions, Julia sets, and canonical local heightsof and . We use this information to completely characterize and in the following cases: (i) and are polynomial mapsin one variable; (ii) is the dth-power map; (iii) is a Lattèsmap. 相似文献
11.
A bifurcation problem governed by the boundary condition II 总被引:1,自引:0,他引:1
Garcia-Melian Jorge; Rossi Julio D.; Sabina De Lis Jose C. 《Proceedings London Mathematical Society》2007,94(1):1-25
In this work we consider the problem u = a(x)up in on , where is a smooth bounded domain, isthe outward unit normal to , is regarded as a parameter and0 < p < 1. We consider both cases where a(x) > 0 in or a(x) is allowed to vanish in a whole subdomain 0 of . Ourmain results include existence of non-negative non-trivial solutionsin the range 0 < < 1, where 1 is characterized by meansof an eigenvalue problem, uniqueness and bifurcation from infinityof such solutions for small , and the appearance of dead coresfor large enough . 相似文献
12.
Let f: (Rn,0) (Rp,0) be a C map-germ. We define f to be finitely,or -, A-determined, if there exists an integer m such that allgerms g with jmg(0) = jmf(0), or if all germs g with the sameinfinite Taylor series as f, respectively, are A-equivalentto f. For any integer k, 0 k < , we can consider A' sCkcounterpart (consisting of Ck diffeomorphisms) A(k), and wecan define the notion of finite, or -,A(k)-determinacy in asimilar manner. Consider the following conditions for a C germf: (ak) f is -A(k)-determined, (bk) f is finitely A(k)-determined,(t) , (g) there exists a representative f : U Rp defined on some neighbourhood U of 0 in Rn such thatthe multigerm of f is stable at every finite set , and (g') every f' with j f'(0)=j f(0) satisfiescondition (g). We also define a technical condition which willimply condition (g) above. This condition is a collection ofp+1 Lojasiewicz inequalities which express that the multigermof f is stable at any finite set of points outside 0 and onlybecomes unstable at a finite rate when we approach 0. We willdenote this condition by (e). With this notation we prove thefollowing. For any C map germ f:(Rn,0) (Rp,0) the conditions(e), (t), (g') and (a) are equivalent conditions. Moreover,each of these conditions is equivalent to any of (ak) (p+1 k < , (bk) (p+1 k < ). 1991 Mathematics Subject Classification:58C27. 相似文献
13.
Let H be the discrete Schrödinger operator acting on l2 Z+, where the potential v is real-valued and v(n) 0 as n . Let P be the orthogonal projection onto a closedlinear subspace l2 Z+). In a recent paper E. B. Davies definesthe second order spectrum Spec2(H, ) of H relative to as theset of z C such that the restriction to of the operator P(H- z)2P is not invertible within the space . The purpose of thisarticle is to investigate properties of Spec2(H, ) when islarge but finite dimensional. We explore in particular the connectionbetween this set and the spectrum of H. Our main result providessharp bounds in terms of the potential v for the asymptoticbehaviour of Spec2(H, ) as increases towards l2 Z+). 2000 MathematicsSubject Classification 47B36 (primary), 47B39, 81-08 (secondary). 相似文献
14.
In this paper we obtain uniform estimates for the lattice pointproblem in the hyperbolic plane H under the assumption thatthe action is by a Fuchsian group which is co-finite. We fixa point w from H and set Nt(z, w) equal to the number of translatesof w by the group which lie in a geodesic ball of radius tcentred at a point z of H. The behaviour of Nt(z, w) is thenexamined when t is large and z is allowed to vary over H. Weshow that the finite quantity depends crucially on the point w, and indeed can become arbitrarilylarge with w. On the other hand, for the average of this quotientwe derive the estimate as t , where the implied constant is an explicit function ofw. In this formula, vol(F) is the hyperbolic volume of a Dirichletfundamentaldomain F for , and |w| denotes the number of elements from fixing w. This estimate is then combined with a recent samplingtheorem of K. Seip to obtain an inequality which decides whetheror not the orbit . w forms a set of interpolation for a givenweighted Bergman space in H. 1991 Mathematics Subject Classification:11F72, 11P21, 30D35, 30E05, 30F35. 相似文献
15.
General Uniqueness Results and Variation Speed for Blow-Up Solutions of Elliptic Equations 总被引:7,自引:0,他引:7
Let be a smooth bounded domain in RN. We prove general uniquenessresults for equations of the form u = au b(x)f(u) in , subject to u = on . Our uniqueness theorem is establishedin a setting involving Karamata's theory on regularly varyingfunctions, which is used to relate the blow-up behavior of u(x)with f(u) and b(x), where b 0 on and a certain ratio involvingb is bounded near . A key step in our proof of uniqueness usesa modification of an iteration technique due to Safonov. 2000Mathematics Subject Classification 35J25 (primary), 35B40, 35J60(secondary). 相似文献
16.
Weighted Triebel–Lizorkin and Besov spaces on the unitball Bd in d with weights wµ(x)=(1–|x|2)µ–1/2,µ0, are introduced and explored. A decomposition schemeis developed in terms of almost exponentially localized polynomialelements (needlets) {}, {} and it is shown that the membershipof a distribution to the weighted Triebel–Lizorkin orBesov spaces can be determined by the size of the needlet coefficients{f, } in appropriate sequence spaces. 相似文献
17.
18.
Hopf C*-Algebras 总被引:1,自引:0,他引:1
In this paper we define and study Hopf C*-algebras. Roughlyspeaking, a Hopf C*-algebra is a C*-algebra A with a comultiplication: A M(A A) such that the maps a b (a)(1 b) and a (a 1)(b)have their range in A A and are injective after being extendedto a larger natural domain, the Haagerup tensor product A hA. In a purely algebraic setting, these conditions on are closelyrelated to the existence of a counit and antipode. In this topologicalcontext, things turn out to be much more subtle, but neverthelessone can show the existence of a suitable counit and antipodeunder these conditions. The basic example is the C*-algebra C0(G) of continuous complexfunctions tending to zero at infinity on a locally compact groupwhere the comultiplication is obtained by dualizing the groupmultiplication. But also the reduced group C*-algebra of a locally compact group with thewell-known comultiplication falls in this category. In factall locally compact quantum groups in the sense of Kustermansand the first author (such as the compact and discrete ones)as well as most of the known examples are included. This theory differs from other similar approaches in that thereis no Haar measure assumed. 2000 Mathematics Subject Classification: 46L65, 46L07, 46L89. 相似文献
19.
Cascante Carme; Ortega Joaquin M.; Verbitsky Igor E. 《Proceedings London Mathematical Society》2000,80(2):391-414
We give a new non-capacitary characterization of positive Borelmeasures µ on Rn such that the potential space I*Lp isimbedded in Lq(dµ) for $1qp+, that is, the trace inequality holds, for Riesz potentials I = (- )2. A weak-type trace inequality is also characterized. A non-isotropic version on the unit sphere Sn is studied,as well as the holomorphic case for HardySobolev spaces in the ball. 1991 MathematicsSubject Classification: primary 31C15, 42B20; secondary 32A35. 相似文献
20.
Let F be a non-Archimedean local field, with the ring of integersoF. Let G = GLN(F), K = GLN (oF), and be a supercuspidal representationof G. We show that there exists a unique irreducible smoothrepresentation of K, such that the restriction to K of a smoothirreducible representation ' of G contains if and only if 'is isomorphic to ° det, where is an unramified quasicharacterof Fx. Moreover, we show that contains with the multiplicity1. As a corollary we obtain a kind of inertial local Langlandscorrespondence. 2000 Mathematics Subject Classification 22E50. 相似文献