Đề tài "A sharp form of Whitney’s extension theorem " ppt

... C  determined by A, m, n.(8) Annals of Mathematics A sharp form of Whitney’s extension theorem By Charles L. Fefferman A SHARP FORM OF WHITNEY’S EXTENSION THEOREM 527 From (1), ,(5), we ... that J y (ϕ S α )=P y α for all α ∈A.(24) The conclusions of the lemma are (19), (20), (22), (23), (24). The proof of Lemma 10.3 is complete. A SHARP FORM...

Ngày tải lên: 29/03/2014, 07:20

... proof as well as Chernoff’s proof is based on an expansion of f in Hermite polynomials (or tensor products of Hermite polynomials in the case N ≥ 2). Chen gives in [Cn] a self-contained proof ... that ϕ(x i )=y i ,i=1, 2, ,r. Before the proof of Theorem 2.2, we make a few observations: 2.3 Remark. (1) In connection with condition (2.1) above, let V be a subspace of M m (C) containing...

Ngày tải lên: 22/03/2014, 20:20

... ερ)) ρ∈[0,4] of Bohr sets, where Γ ⊆  G is a set of characters. It turns out not to be much harder to deal with the join of a pair of Bourgain systems in general. Definition 4.9 (Joining of two Bourgain ... equivalent to the lower bound on the size of S ∧S  that we claimed. We move on now to one of the more technical aspects of the theory of Bourgain systems, the notion of...

Ngày tải lên: 22/03/2014, 20:21

... over Q ), we can rewrite Theorem 4.1 of [Mi5] into the following theorem. Theorem 3.25. Under Hypotheses I, V =  α∈S V α has a structure of (D, S)-framed VOA with a PDIB -form. A framed VOA structure ... 2-group. Let V = ⊕ χ∈Irr(Q) V χ be the decomposition of V into the direct sum of eigenspaces of Q, where Irr(Q) is the set of linear characters of Q. Since dim V 0 = 1 and...

Ngày tải lên: 28/03/2014, 22:20

... irreducible components of |C n | and of |C ∞ | respecting the genera. Proof. By the definition of the cycle topology, for n  0 each component of C ∞ deforms to parts of some component of C n . This sets ... as the virtual num- ber of double points. This is the number of nodes of the image of a small, general, J-holomorphic deformation of the parametrization map from a un...

Ngày tải lên: 16/02/2014, 05:20

... Thus, 2ε AB R A43B = −ε AB R AB43 . In view of Corollary 4.6 we can therefore express ε AB R A43B in the form curl/π (2) + E (2) . 5. Strategy of the proof of the Asymptotics Theorem In this section we describe ... assumption B2). We shall next formulate versions of the Calderon-Zygmund theorem for the above types of Hodge systems; see also [B-W]. The proof is a straightforwar...

Ngày tải lên: 16/02/2014, 05:20

... to isotope Γ so as to reduce the number of points of intersection of that part of the graph in the boundary of the singular disk which is the extension of E. After finitely many steps, we have ... interior of W. Let S denote the collection of ends of planes and catenoids defined above which arises from the collection of nonsimply connected components W of H i −∪D i . It...

Ngày tải lên: 16/02/2014, 06:20

... triangles of G, and if A = {1, 2, 3}, say, then H ∗ (A) consists of all triangles in G with one vertex in each of X 1 , X 2 and X 3 , while H(A) consists of all 3-edges of H with one vertex in each of ... bounded number of pieces, almost all of which are quasiran- dom. This generalizes Szemer´edi’s regularity lemma for graphs (which formed part of his proof of his theorem...

Ngày tải lên: 22/03/2014, 20:21

... result. Annals of Mathematics A proof of Kirillov’s conjecture By Ehud Moshe Baruch* APROOF OF KIRILLOV’S CONJECTURE 225 The proof of Lemma 5.2 is an easy consequence of the description of ... Jacobson-Morosov triple. Set G =GL n (K). The G conjugacy class of X ∈ is the set of elements of of the form O G (X)={gXg −1 | g ∈ G}. The G conjugacy class of X is...

Ngày tải lên: 28/03/2014, 22:20

... Department of Structural and Functional Biology, and Centre of Neuroscience, University of Insubria, Busto Arsizio, Italy 2 Department of Biotechnology, University of Verona, Italy 3 Department of Clinical ... familial forms of PD [6]. However, a-synuclein deposition into LB is a general hallmark of the PD state, suggesting that the accumula- tion of a-synuclein might cause...

Ngày tải lên: 15/02/2014, 01:20