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作者：Mateu, Joan; Orobitg, Joan; Verdera, Joan
摘要：Let T be a smooth homogeneous Calderon-Zygmund singular integral operator in R-n. In this paper we study the problem of controlling the maximal singular integral T* f by the singular integral T f. The most basic form of control one may consider is the estimate of the L-2 (R-n) norm of T* f by a constant times the L-2 (R-n) norm of T f. We show that if T is an even higher order Riesz transform, then one has the stronger pointwise inequality T* f(x) <= C M(T f)(x), where C is a constant and M is...
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作者：Marklof, Jens; Strombergsson, Andreas
摘要：We study the dynamics of a point particle in a periodic array of spherical scatterers and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit). A generic path of the limiting process is a piecewise linear curve whose consecutive segments are generated by a Markov process with memory two.
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作者：Ulcigrai, Corinna
摘要：We prove that minimal area-preserving flows locally given by a 3smooth Hamiltonian on a closed surface of genus g <= 2 are typically (in the measure-theoretical sense) not mixing. The result is obtained by cons idering special flows over interval exchange transformations under roof functions with symmetric logarithmic singularities and proving absence of mixing for a full measure set of interval exchange transformations.
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作者：Aldaz, J. M.
摘要：Let M-d be the centered Hardy-Littlewood maximal function associated to cubes in R-d with Lebesgue measure, and let c(d) denote the lowest constant appearing in the weak type (1, 1) inequality satisfied by M-d. We show that c(d)->infinity as d ->infinity, thus answering, for the case of cubes, a longstanding open question of E. M. Stein and J. O. Stromberg.
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作者：Duke, W.; Imamoglu, Oe.; Toth, A.
摘要：In this paper we construct certain mock modular forms of weight 1/2 whose Fourier coefficients are given in terms of cycle integrals of the modular j-function. Their shadows are weakly holomorphic forms of weight 3/2. These new mock modular forms occur as holomorphic parts of weakly harmonic Maass forms. We also contruct a generalized mock modular form of weight 1/2 having a real quadratic class number times a regulator as a Fourier coefficient. As an application of these forms we study holomo...
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作者：Herscovich, Estanislao; Solotar, Andrea
摘要：The aim of this article is to describe families of representations of the Yang-Mills algebras YM(n) (n is an element of N->= 2) defined by A. Connes and M. Dubois-Violette. We first describe some irreducible finite dimensional representations. Next, we provide families of infinite dimensional representations of YM, big enough to seperate points of the algebra. In order to prove this result, we prove and use that all Weyl algebras A(r)(k) are epimorphic images of YM(n).
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作者：Kaczorowski, Jerzy; Perelli, Alberto
摘要：The Selberg class S is a rather general class of Dirichlet series with functional equation and Euler product and can be regarded as an axiomatic model for the global L-functions arising from number theory and automorphic representations. One of the main problems of the Selberg class theory is to classify the elements of S. Such a classification is based on a real-valued invariant d called degree, and the degree conjecture asserts that d is an element of N for every L-functionin S. The degree c...
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作者：Cheung, Yitwah
摘要：In this paper we show that the Hausdorff dimension of the set of singular pairs is 4/3. We also show that the action of diag(e(t), e(t), e(-2t)) on SL3R/SL(3)Z admits divergent trajectories that exit to infinity at arbitrarily slow prescribed rates, answering a question of A. N. Starkov. As a by-product of the analysis, we obtain a higher-dimensional generalization of the basic inequalities satisfied by convergents of continued fractions. As an illustration of the technique used to compute Hau...
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作者：Lev, Nir; Olevskii, Alexander
摘要：N. Wiener characterized the cyclic vectors (with respect to translations) in l(p)(Z) and L-p (R), p = 1,2, in terms of the zero set of the Fourier transform. He conjectured that a similar characterization should be true for 1 < p < 2. Our main result contradicts this conjecture.
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作者：Gan, Wee Teck; Takeda, Shuichiro
摘要：We prove the local Langlands conjecture for GSp(4) (F) where F is a non-archimedean local field of characteristic zero.
