Annals of Mathematics

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• Discrete analogues in harmonic analysis: Spherical averages AI翻译
  作者：Magyar, A; Stein, EM; Wainger, S
  摘要：In this paper we prove an analogue in the discrete setting of Z(d), of the spherical maximal theorem for R-d. The methods used are two-fold: the application of certain sampling techniques, and ideas arising in the study of the number of representations of an integer as a sum of d squares, in particular, the circle method. The results we obtained are by necessity limited to d greater than or equal to 5, and moreover the range of p for the L-p estimates differs from its analogue in R-d.
• On asymptotic volume of Finsler tori, minimal surfaces in normed spaces, and symplectic filling volume AI翻译
  作者：Burago, D; Ivanov, S
• Positive noncommutative polynomials are sums of squares AI翻译
  作者：Helton, JW
  摘要：Hilbert's 17th problem concerns expression of polynomials on R-n as a sum of squares. It is well known that many positive polynomials are not sums of squares; see [Re], [D'A] for excellent surveys. In this paper we consider symmetric noncommutative polynomials and call one matrix-positive, if whenever matrices of any size are substituted for the variables in the polynomial the matrix value which the polynomial takes is positive semidefinite. The result in this paper is: A polynomial is matrix-...
• The density of rational points on curves and surfaces AI翻译
  作者：Heath-Brown, DR
• Deviation of ergodic averages for area-preserving flows on surfaces of higher genus AI翻译
  作者：Forni, G
• A structure theorem for actions of semisimple Lie groups AI翻译
  作者：Nevo, A; Zimmer, RJ
  摘要：We consider a connected semisimple Lie group G with finite center, an admissible probability measure mu on G, and an ergodic (G, mu)-space (X, nu). We first note (Lemma 0.1) that (X, nu) has a unique maximal projective factor of the form (G/Q, nu(0)), where Q is a parabolic subgroup of G, and then prove: 1. Theorem 1. If every noncompact simple factor of G has real rank at least two, then the maximal projective factor is nontrivial, unless nu is a G-invariant measure. 2. Theorem 2. For any G o...
• Rational maps are d-adic Bernoulli AI翻译
  作者：Heicklen, D; Hoffman, C
  摘要：Freire, Lopes and Mane proved that for any rational map f there exists a natural invariant measure mu(f) [5]. Mane showed there exists an n > 0 such that (f(n), mu(f)) is measurably conjugate to the one-sided d(n)-shift, with Bernoulli measure (1/d(n),...,1/d(n)) [15]. In this paper we show that (f, mu(f)) is conjugate to the one-sided Bernoulli d-shift. This verifies a conjecture of Freire, Lopes and Mane [5] and Lyubich [11].
• Rational functions with real critical points and the B. and M.!Shapiro conjecture in real enumerative geometry AI翻译
  作者：Eremenko, A; Gabrielov, A
  摘要：Suppose that 2d - 2 tangent lines to the rational normal curve z --> (1 : z : ... z(d)) in d-dimensional complex projective space are given. It was known that the number of codimension 2 subspaces intersecting all these lines is always finite; for a generic configuration it is equal to the d(th) Catalan number. We prove that for real tangent lines, all these codimension 2 subspaces are also real, thus confirming a special case of a general conjecture of B. and M. Shapiro. This is equivalent to...
• Extension of embeddings in the computably enumerable degrees AI翻译
  作者：Slaman, TA; Soare, RI
• On the nonexistence of tight contact structures AI翻译
  作者：Etnyre, JB; Honda, K