Đề tài "The Schr¨odinger propagator for scattering metrics " pdf

... x 2 h ij M i M j  . Annals of Mathematics The Schr¨odinger propagator for scattering metrics By Andrew Hassell and Jared Wunsch SCHR ¨ ODINGER PROPAGATOR 505 This implies that d(z,w)= 1 x − ... follows Annals of Mathematics, 162 (2005), 487–523 The Schr¨odinger propagator for scattering metrics By Andrew Hassell and Jared Wunsch* Abstract Let g be a scat...

Ngày tải lên: 15/03/2014, 09:20

... bilinear form satisfying (2.9) b ψ U (ω ψ (u, h)ϕ, π ∨ m (h)ξ)=ψ U (u)b ψ U (ϕ, ξ) for u ∈ U n , h ∈  Sp 2m (k), ϕ ∈S(V m ), ξ ∈ V π ∨ m .Wewill show that, for m<n, the space of bilinear forms, ... Converse Theorem for GL(n). We refer to [CP-S1] and [CP-S2] for detailed explanation of converse theorems. The local converse theorem for the general linear group, GL(n), was first for...

Ngày tải lên: 22/03/2014, 15:21

... Write  γ k g and THE CALABI-YAU CONJECTURES FOR EMBEDDED SURFACES 235  γ i k g for the two boundary terms in the Gauss-Bonnet theorem for the annulus Γ i (both are uniformly bounded;  γ i k g is after ... div(a∇u)+b, ∇u +(c −1)|A| 2 u,(3.14) for functions a ij , b j , c on Σ with |a|, |c|≤3 |A||u|+ |∇u| and |b|≤2 |A||∇u|. Equation (3.14) implies a uniform Harnack inequality for...

Ngày tải lên: 29/03/2014, 07:20

... a Gowers uniform component and a Gowers anti-uniform component. We will come to this splitting in later sections, but for this section we focus on defining the notion of Gowers uniformity, intro- duced ... Lemma 2.2]), where the Fourier transform ˆ f : Z N → C of f is defined by the formula 12  f(ξ):=E(f(x)e −2πixξ/N |x ∈ Z N ). for any ξ ∈ Z N . 12 The Fourier transform of course plays a...

Ngày tải lên: 29/03/2014, 07:20

... t) (22) for some universal constant C ∗ > 0. This bound is optimal for NLS in the sense that there exist blow-up solutions with this blow-up rate. Indeed, apply the pseudoconformal transformation ... is also Galilean invariance and pseudoconformal transformation, to a priori get rid of these directions. Note nevertheless that as the pseudoconformal trans- formation is not in the energy...

Ngày tải lên: 29/03/2014, 07:20

... A (n) (are defined and) converge to A uniformly on V . We recall that the weak topology is metrizable for r = ω, but not even separable for r = ω. REDUCIBLE OR NONUNIFORMLY HYPERBOLIC SCHR ¨ ODINGER ... Mathematics Reducibility or nonuniform hyperbolicity for quasiperiodic Schr¨odinger cocycles By Artur Avila* and Rapha¨el Krikorian REDUCIBLE OR NONUNIFORMLY HYPERBOLIC S...

Ngày tải lên: 22/03/2014, 20:20

... in [24] serve as good concise references on the subject. See [15] for information on the Mapping Reflection Principle. For basic forcing technology, the reader is referred to [11] and [14]. Part ... N r 0 . Let k = |N r \ N r 0 | and ζ be the maximum of all ordinals of the forms ht(s) + 1 for s ∈ X r 0 and N ∩ ω 1 for N ∈ N r 0 . Let T k be the set of all q ≤ r 0 in D such that: (11) X...

Ngày tải lên: 06/03/2014, 08:21

... Section 3.2). Therefore, in Theorem 4.9 both ρ and ε are zero. This gives us the formulas in part (a) and (b). Part (c) is Proposition 4.6. THE HOPF CONDITION FOR BILINEAR FORMS 947 For us, the most ... before, let j be the inclusion Annals of Mathematics The Hopf condition for bilinear forms over arbitrary fields By Daniel Dugger and Daniel C. Isaksen THE HOPF CONDITIO...

Ngày tải lên: 06/03/2014, 08:21

... be a left Banach G-module for which the action of G is uniformly bounded. (a) The bidual X  becomes a left βG-module, extending the action of G on X and such that for every fixed x ∈ G the mapping ... βG. If the action of G on X is uniformly bounded and continuous (i.e., x → x ◦ v is continuous for each v ∈ X ), then it is easy to see that p ◦ v depends for v ∈ X only on the image o...

Ngày tải lên: 06/03/2014, 08:21

... length    J + i ∩ J − j    since a i /∈ J j for every s<j≤ r i . Similar considerations can be applied if a i ∈ J + s for some l i ≤ s<i. Finally for any special interval I p,q where a q /∈ ... 9. Some of those are of course 0 as explained above, for example d 4,6 = d 5,9 =0. Also we have given bounds for all five sums  j d i,j , for example  j d 4,j ≤ b − 1. Now it i...

Ngày tải lên: 14/03/2014, 22:20