共查询到20条相似文献,搜索用时 171 毫秒
1.
Translation representation for automorphic solutions of the wave equation in non-euclidean spaces,IV
In Part I of this series of papers we have defined the incoming and outgoing translation representations for automorphic solutions of the hyperbolic wave equations; in Part II we have proved the completeness of these representations when the fundamental polyhedron F has a finite number of sides with a finite or infinite volume, but is not compact. In Part IV we present a proof of completeness which is simpler than our original proof contained in Section 7 of Part II for the case when F has cusps of less than maximal rank; and we supply a proof for the case, not covered in Section 7, when the parabolic subgroup associated with such cusps contains twists. 相似文献
2.
Summary Let Fn, n≧ 1, denote the sequence of generic filiform (connected, simply connected) Lie groups. Here we study, for each Fn, the infinite dimensional simple quotients of the group C*-algebra of (the most obvious) one of its discrete cocompact subgroups Dn. For Dn, the most attractive concrete faithful representations are given in terms of Anzai flows, in analogy with the representations
of the discrete Heisenberg group H3 ⊆G3 on L2(T) that result from the irrational rotation flows on T; the representations of Dn generate infinite-dimensional simple quotients An,θ of the group C*-algebra C*(Dn). For n>1, there are other infinite-dimensional simple quotients of C*(Dn) arising from non-faithful representations of Dn. Flows for these are determined, and they are also characterized and represented as matrix algebras over simple affine Furstenberg
transformation group C*-algebras of the lower dimensional tori. 相似文献
3.
ON THE DIFFUSION PHENOMENON OF QUASILINEAR HYPERBOLICWAVES 总被引:1,自引:0,他引:1
YANG Han 《数学年刊B辑(英文版)》2000,21(1):63-70
Introduction1.1.ConsiderthefollowingquasilinearhyperbolicCauchyproblemwithlineardamping{:;;!OTt=-:i<:,;>>L06,(11)wherexER",t20,anda(.)isasmoothfunctionsatisfyinga(y)~1 O(lyl")aslyl-0,orEN.(1.2)Thepurposeofthispaperistoshowthat,atleastwhenn53,theasymptoticprofileofthesolutionu(x,t)of(l.1)isgivenbythesolutionv(x,t)ofthecorrespondingparabolicproblem{:;.t>ivj:相似文献
4.
Guy Henniart 《Inventiones Mathematicae》2000,139(2):439-455
Let F be a finite extension of ℚ
p
. For each integer n≥1, we construct a bijection from the set ?F
0
(n) of isomorphism classes of irreducible degree n representations of the (absolute) Weil group of F, onto the set ?
F
0
(n) of isomorphism classes of smooth irreducible supercuspidal representations of GL
n
(F). Those bijections preserve epsilon factors for pairs and hence we obtain a proof of the Langlands conjectures for GL
n
over F, which is more direct than Harris and Taylor’s. Our approach is global, and analogous to the derivation of local class field
theory from global class field theory. We start with a result of Kottwitz and Clozel on the good reduction of some Shimura
varieties and we use a trick of Harris, who constructs non-Galois automorphic induction in certain cases.
Oblatum 1-III-1999 & 21-VII-1999 / Published online: 29 November 1999 相似文献
5.
Tatyana Foth 《Differential Geometry and its Applications》2008,26(1):63-74
Let X be CPn or a compact smooth quotient of the n-dimensional complex hyperbolic space, n>1. Let L be a hermitian holomorphic line bundle (with hermitian connection) on X chosen as follows: if X=CPn then L is the hyperplane bundle, and in the second case L is chosen so that L⊗(n+1)=KX⊗E, where KX is the canonical line bundle and E is a flat line bundle. The unit circle bundle P in L∗ is a contact manifold. Let k′ be a fixed positive integer. We construct certain Legendrian tori in P (the construction depends, in particular, on the choice of k′) and sequences {uk}, k=k′m, , of holomorphic sections of L⊗k associated to these tori. We study asymptotics of the norms ‖ukk‖ as m→+∞ and, in particular, apply this result to construct explicitly certain non-trivial holomorphic automorphic forms on the n-dimensional complex hyperbolic space. We obtain an n>1 analogue of the classical period formula (this is a well-known statement for automorphic forms on the upper half plane, n=1). 相似文献
6.
We shall show an exact time interval for the existence of local strong solutions to the Keller‐Segel system with the initial data u0 in Ln /2w (?n), the weak Ln /2‐space on ?n. If ‖u0‖ is sufficiently small, then our solution exists globally in time. Our motivation to construct solutions in Ln /2w (?n) stems from obtaining a self‐similar solution which does not belong to any usual Lp(?n). Furthermore, the characterization of local existence of solutions gives us an explicit blow‐up rate of ‖u (t)‖ for n /2 < p < ∞ as t → Tmax, where Tmax denotes the maximal existence time (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
The singularly perturbed two‐well problem in the theory of solid‐solid phase transitions takes the form where u : Ω ? ?n → ?n is the deformation, and W vanishes for all matrices in K = SO(n)A ∪ SO(n)B. We focus on the case n = 2 and derive, by means of Gamma convergence, a sharp‐interface limit for Iε. The proof is based on a rigidity estimate for low‐energy functions. Our rigidity argument also gives an optimal two‐well Liouville estimate: if ?u has a small BV norm (compared to the diameter of the domain), then, in the L1 sense, either the distance of ?u from SO(2)A or the one from SO(2)B is controlled by the distance of ?u from K. This implies that the oscillation of ?u in weak L1 is controlled by the L1 norm of the distance of ?u to K. © 2006 Wiley Periodicals, Inc. 相似文献
8.
Vitali Chkliar 《Integral Equations and Operator Theory》1997,29(3):364-367
Letu inH
2 be zero at one of the fixed points of a hyperbolic Möbius transform of the unit diskD. We will show, under some additional conditions onu, that the doubly cyclic subspaceS
u
=V
n=–
C
n
u contains nonconstant eigenfunctions of the composition operatorC
. This implies that the cyclic subspace generated byu is not minimal. If there is an infinite dimensional minimal invariant subspace ofC
(which is equivalent to the existance of an operator with only trivial invariant subspaces), then it is generated by a function with singularities at the fixed points of . 相似文献
9.
Kosuke Ono 《Journal of Mathematical Analysis and Applications》2005,310(2):347-361
Consider the Cauchy problem in odd dimensions for the dissipative wave equation: (□+∂t)u=0 in with (u,∂tu)|t=0=(u0,u1). Because the L2 estimates and the L∞ estimates of the solution u(t) are well known, in this paper we pay attention to the Lp estimates with 1p<2 (in particular, p=1) of the solution u(t) for t0. In order to derive Lp estimates we first give the representation formulas of the solution u(t)=∂tS(t)u0+S(t)(u0+u1) and then we directly estimate the exact solution S(t)g and its derivative ∂tS(t)g of the dissipative wave equation with the initial data (u0,u1)=(0,g). In particular, when p=1 and n1, we get the L1 estimate: u(t)L1Ce−t/4(u0Wn,1+u1Wn−1,1)+C(u0L1+u1L1) for t0. 相似文献
10.
We show that the supremum norm of solutions with small initial data of the generalized Benjamin-Bona-Mahony equation ut-△ut=(b,▽u)+up(a,▽u)in x?Rn,n≥2, with integer p≥3 , decays to zero like t-2/3 if n=2 and like t-1+6, for any δ0, if n≥3, when t tends to infinity. The proofs of these results are based on an analysis of the linear equation ut-△=(b,▽u)) and the associated oscillatory integral which may have nonisolated stationary points of the phase function. 相似文献
11.
Yuri Yu. Berest 《纯数学与应用数学通讯》1997,50(10):1019-1052
We give a complete solution of Hadamard's problem concerning Huygens' principle on even-dimensional Minkowski spaces 𝕄n+1 for a restricted class of linear, second-order, normal hyperbolic operators ℒ︁ = □n+1 + u(x1, x2) with real (locally) analytic potentials u = u(x1, x2) depending on two spatial variables and homogeneous of degree −2. © 1997 John Wiley & Sons, Inc. 相似文献
12.
Pham Huu Tiep 《Geometriae Dedicata》1997,64(1):85-123
The notion of globally irreducible representations of finite groups has been introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell--Weil lattices of elliptic curves. In this paper we first give a necessary condition for global irreducibility. Then we classify all globally irreducible representations of L
2(q) and 2B2(q), and of the majority of the 26 sporadic finite simple groups. We also exhibit one more globally irreducible representation, which is related to the Weil representation of degree (pn-1)/2 of the symplectic group Sp2n(p) (p 1 (mod 4) is a prime). As a consequence, we get a new series of even unimodular lattices of rank 2(pn–1). A summary of currently known globally irreducible representations is given. 相似文献
13.
We prove a local normal form theorem of the Gaifman type for the infinitary logic L∞ω( Q u)ω whose formulas involve arbitrary unary quantifiers but finite quantifier rank. We use a local Ehrenfeucht‐Fraïssé type game similar to the one in [9]. A consequence is that every sentence of L∞ω( Q u)ω of quantifier rank n is equivalent to an infinite Boolean combination of sentences of the form (?≥iy)ψ(y), where ψ(y) has counting quantifiers restricted to the (2n–1 – 1)‐neighborhood of y. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
Kosuke Ono 《Mathematical Methods in the Applied Sciences》2004,27(16):1843-1863
We study Lp decay estimates of the solution to the Cauchy problem for the dissipative wave equation in even dimensions: (□+?t)u=0 in ?N × (0,∞) for even N=2n?2 with initial data (u,?tu)∣t=0 =(u0,u1). The representation formulas of the solution u(t)=?tS(t)u0 + S(t)(u0+u1) provide the sharp estimates on Lp norms with p?1. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
Let (m, n) ∈ ℕ2, Ω an open bounded domain in ℝm , Y = [0, 1]m ; uε in (L2(Ω))n which is two-scale converges to some u in (L2(Ω × Y))n . Let φ: Ω × ℝm × ℝn → ℝ such that: φ(x, ·, ·) is continuous a.e. x ∈ Ω φ(·, y, z) is measurable for all (y, z) in ℝm × ℝn , φ(x, ·, z) is 1-periodic in y, φ(x, y, ·) is convex in z. Assume that there exist a constant C1 > 0 and a function C2 ∈ L2(Ω) such that
16.
T. Shibata 《Annales Henri Poincare》2001,2(4):713-732
17.
The paper studies the existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation arising in the model in variational form for the neo–Hookean elastomer rod where k1, k2>0 are real numbers, g(s) is a given nonlinear function. When g(s)=sn (where n?2 is an integer), by using the Fourier transform method we prove that for any T>0, the Cauchy problem admits a unique global smooth solution u∈C∞((0, T]; H∞( R ))∩C([0, T]; H3( R ))∩C1([0, T]; H?1( R )) as long as initial data u0∈W4, 1( R )∩H3( R ), u1∈L1( R )∩H?1( R ). Moreover, when (u0, u1)∈H2( R ) × L2( R ), g∈C2( R ) satisfy certain conditions, the Cauchy problem has no global solution in space C([0, T]; H2( R ))∩C1([0, T]; L2( R ))∩H1(0, T; H2( R )). Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
18.
Let V be an r-dimensional vector space over an infinite field F of prime characteristic p, and let Ln(V) denote the nth homogeneous component of the free Lie algebra on V. We study the structure of Ln(V) as a module for the general linear group GLr(F) when n=pk and k is not divisible by p and where r≥n. Our main result is an explicit 1-1 correspondence, multiplicity-preserving, between the indecomposable direct summands of
Lk(V) and the indecomposable direct summands of Ln(V) which are not isomorphic to direct summands of V⊗n. Our approach uses idempotents of the Solomon descent algebras, and in addition a correspondence theorem for permutation
modules of symmetric groups.
Second author supported by Deutsche Forschungsgemeinschaft (DFG-Scho 799). 相似文献
19.
Emrah Kilic 《Proceedings Mathematical Sciences》2008,118(1):27-41
In this paper, we consider generalized Fibonacci type second order linear recurrence {u
n
}. We derive a generating matrix for both the sums of squares, ∑
i=0
n
u
i
2 and the products of the form u
n
u
n+2. We also derive explicit formulas for the sums and products by using matrix methods. Then we give a matrix method to generate
the sums of product of two consecutive terms u
n
u
n+1 as well as the product, u
n
u
n+2. Further we give generating functions and combinatorial representations of the sums of squares of terms of {u
n
} and the product, u
n
u
n+2. 相似文献
20.
A. Müller-Rettkowski 《Monatshefte für Mathematik》1983,96(2):143-156
In a bounded simply-connected domainG \( \subseteq \) ?2 a boundary value problem for a linear partial differential equation of second orderLu=f is studied. The operatorL is elliptic inG?{y>0}, parabolic forG?{y=0} and hyperbolic inG?{y<0}. The boundary value problem consists in findingu satisfyingLu=f inG, d n u=φ on the elliptic part of the boundary ofG, u=ψ on the noncharacteristic part (which is not empty) of the hyperbolic part of the boundary ofG.d n u denotes the conormal (with respect toL) derivative ofu. It is proved that the problem has a generalized solution in anL 2-weight space. Uniqueness is otained in the class of quasiregular solutions. In order to get the results apriori estimates are proved; theorems from functional analysis are used. 相似文献