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作者：Ash, JM; Wang, G
摘要：We prove that if a multiple trigonometric series is spherically Abel summable everywhere to an everywhere finite function f(x) which is bounded below by an integrable function, then the series is the Fourier series of f(x) if the coefficients of the multiple trigonometric series satisfy a mild growth condition. As a consequence, we show that if a multiple trigonometric series is spherically convergent everywhere to an everywhere finite integrable function f(x), then the series is the Fourier s...
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作者：Kaimanovich, VA
摘要：The Poisson boundary of a group G with a probability measure mu is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an integral representation of bounded mu -harmonic functions on G. In this paper we develop a new method of identifying the Poisson boundary based on entropy estimates for conditional random walks. It leads to simple purely geometric criteria of boundary maximality whi...
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作者：Ionescu, AD
摘要：One of the purposes of this paper is to prove that if G is a noncompact connected semisimple Lie group of real rank one with finite center, then L-2,L-1(G)*L-2,L-1(G) subset of or equal to L-2,L-infinity(G). Let K be a maximal compact subgroup of G and X = G/K a symmetric space of real rank one. We will also prove that the noncentered maximal operator M(2)f(z) = sup(z epsilonB)1//B/ integral (B)/f(z')/dz' is bounded from L-2,L-1(X) to L-2,L-infinity(X) and from L-P(X) to L-P(X) in the sharp ra...
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作者：Fefferman, C
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作者：Tian, G
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作者：Bonk, M; Eremenko, A
摘要：Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan root8 approximate to 70 degrees 32'. If in addition all critical points of the function are multiple, then a similar statement holds with pi /2. These constants are the best possible. The proof is based on the consideration of negatively curved singular surfaces associated with meromorphic functions.
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作者：Khanin, WEK; Mazel, A; Sinai, Y
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作者：Totaro, B
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作者：Gallo, D; Kapovich, M; Marden, A
摘要：Let theta : pi(1)(R) --> PSL(2, C) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem.
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作者：Sideris, TC
