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1.
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
2.
Goldston D. A.; Gonek S. M.; Ozluk A. E.; Snyder C. 《Proceedings London Mathematical Society》2000,80(1):31-49
To study the distribution of pairs of zeros of the Riemann zeta-function,Montgomery introduced the function
where is real and T 2, and ' denote the imaginary parts ofzeros of the Riemann zeta-function, and w(u) = 4/(4 + u2). Assumingthe Riemann Hypothesis, Montgomery proved an asymptotic formulafor F() when || 1, and made the conjecture that F() = 1 + o(1)as T for any bounded with || 1. In this paper we use anapproximation for the prime indicator function together witha new mean value theorem for long Dirichlet polynomials andtails of Dirichlet series to prove that, assuming the GeneralizedRiemann Hypothesis for all Dirichlet L-functions, then for any > 0 we have
uniformlyfor and all T T0(). 1991Mathematics Subject Classification: primary 11M26; secondary11P32. 相似文献
3.
Craw Alastair; Maclagan Diane; Thomas Rekha R. 《Proceedings London Mathematical Society》2007,95(1):179-198
For a finite abelian group G GL (n, ), we describe the coherent component Y of the moduli space of-stable McKay quiver representations. This is a not-necessarily-normaltoric variety that admits a projective birational morphism obtained by variation of GeometricInvariant Theory quotient. As a special case, this gives a newconstruction of Nakamura's G-Hilbert scheme HilbG that avoidsthe (typically highly singular) Hilbert scheme of |G|-pointsin . To conclude, we describe the toric fan of Y and hence calculate the quiver representationcorresponding to any point of Y. 相似文献
4.
5.
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
6.
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
7.
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
8.
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
9.
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
10.
We investigate the existence of a weak solution u to the quasilineartwo-point boundary value problem We assume that 1 < p < p ¬ = 2, 0 < a < , andthat f L1(0,a) is a given function. The number k stands forthe k-th eigenvalue of the one-dimensional p-Laplacian. Letp p x/a) denote the eigenfunction associated with 1; then p(kp x/a) is the eigenfunction associated with k. We show the existenceof solutions to (P) in the following cases. (i) When k=1 and f satisfies the orthogonality condition the set of solutions is bounded. (ii) If k=1 and ft L1(0,a) is a continuous family parametrizedby t [0,1], with then there exists some t* [0,1] such that (P) has a solutionfor f = ft*. Moreover, an appropriate choice of t* yields asolution u with an arbitrarily large L1(0,a)-norm which meansthat such f cannot be orthogonal to pp x/a. (iii) When k 2 and f satisfies a set of orthogonality conditionsto p(k p x/a) on the subintervals , again, the set of solutions is bounded. is a continuous family satisfying either or another related condition, then there exists some t* [0,1]such that (P) has a solution for f = ft*. Prüfer's transformation plays the key role in our proofs.2000 Mathematical Subject Classification: primary 34B16, 47J10;secondary 34L40, 47H30. 相似文献
11.
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
12.
A finite Borel measure µ on Rd is called R-O varying withindex F if there exist a GL(Rd)-valued function f varying regularlywith index (F), an increasing function k: (0, ) (0,) with k(t) and k(t + 1)/k(t) c 1 as t , and a -finitemeasure on Rd\0 such that R-O varying measures generalize regularly varying measures introducedby Meerschaert (see M. M. Meerschaert, Regular variationin Rk, Proc. Amer. Math. Soc. 102 (1988) 341348)and have numerous applications in limit theorems for probabilitymeasures. For an R-O varying measure µ and < let
denote the tail- andtruncated moment functions of µ in the direction || =1. The purpose of this paper is to show that R-O variation ofa measure implies sharp bounds on the growth rate of the tail-and truncated moment functions depending on the real parts ofthe eigenvalues of the index F along a compact set of directions.Furthermore, bounds on the ratio of these functions for certainvalues of a and b are obtained. 1991 Mathematics Subject Classification:60B10, 28C15. 相似文献
13.
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
14.
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
15.
Grothendieck's Inequalities for Real and Complex JBW*-Triples 总被引:1,自引:0,他引:1
Peralta Antonio M.; Palacios Angel Rodriguez 《Proceedings London Mathematical Society》2001,83(3):605-625
We prove that, if and >0, if V and W are complex JBW*-triples (with preduals V* andW*, respectively), and if U is a separately weak*-continuousbilinear form on V x W, then there exist norm-one functionals1, 2 V* and 1, 2 W* satisfying
for all (x, y) V x W. Here, for a norm-one functional on acomplex JB*-triple V, |·| stands for the prehilbertianseminorm on V associated to given by for all x W, where z V** satisfies z = |z| =1. We arrive at this form of Grothendieck's inequalitythrough results of C.-H. Chu, B. Iochum, and G. Loupias, andan amended version of the little Grothendieck's inequalityfor complex JB*-triples due to T. Barton and Y. Friedman. Wealso obtain extensions of these results to the setting of realJB*-triples. 2000 Mathematical Subject Classification: 17C65,46K70, 46L05, 46L10, 46L70. 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.
Unknotting Tunnels and Seifert Surfaces 总被引:2,自引:0,他引:2
Let K be a knot with an unknotting tunnel and suppose thatK is not a 2-bridge knot. There is an invariant = p/q Q/2Z,with p odd, defined for the pair (K, ). The invariant has interesting geometric properties. It is oftenstraightforward to calculate; for example, for K a torus knotand an annulus-spanning arc, (K, ) = 1. Although is definedabstractly, it is naturally revealed when K is put in thinposition. If 1 then there is a minimal-genus Seifert surfaceF for K such that the tunnel can be slid and isotoped to lieon F. One consequence is that if (K, ) 1 then K > 1. Thisconfirms a conjecture of Goda and Teragaito for pairs (K, )with (K, ) 1. 2000 Mathematics Subject Classification 57M25,57M27. 相似文献
18.
Let X be a regular separated scheme of finite Krull dimensionand let be the punctured affine n-space over X. We show that the total graded Witt ring of is a free graded module over the totalgraded Witt ring of X with two generators 1 and . The secondgenerator satisfies the equation 2 = 1 when n = 1 and 2 = 0when n 2. 2000 Mathematics Subject Classification 11E81, 19G12. 相似文献
19.
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
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