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Creators/Authors contains: "MAGYAR, ÁKOS"

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  1. ; ; ; (, Advanced Nonlinear Studies)
    Lu, Guozhen (Ed.)
    Abstract We discuss some of our work on averages along polynomial sequences in nilpotent groups of step 2. Our main results include boundedness of associated maximal functions and singular integrals operators, an almost everywhere pointwise convergence theorem for ergodic averages along polynomial sequences, and a nilpotent Waring theorem. Our proofs are based on analytical tools, such as a nilpotent Weyl inequality, and on complex almost-orthogonality arguments that are designed to replace Fourier transform tools, which are not available in the noncommutative nilpotent setting. In particular, we present what we call anilpotent circle methodthat allows us to adapt some of the ideas of the classical circle method to the setting of nilpotent groups. 
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  2. ; (, Analysis & PDE)
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  3. ; ; ; (, Inventiones mathematicae)
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  4. ; (, Analysis & PDE)
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  5. ; ; (, American Journal of Mathematics)
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  6. ; (, Mathematical Proceedings of the Cambridge Philosophical Society)
    Abstract We establish that any subset of ℝ d of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of any fixed two-dimensional rectangle provided d ⩾ 4. We further present an extension of this result to configurations that are the product of two non-degenerate simplices; specifically we show that if Δ k 1 and Δ k 2 are two fixed non-degenerate simplices of k 1 + 1 and k 2 + 1 points respectively, then any subset of ℝ d of positive upper Banach density with d ⩾ k 1 + k 2 + 6 will necessarily contain an isometric copy of all sufficiently large dilates of Δ k 1 × Δ k 2 . A new direct proof of the fact that any subset of ℝ d of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of any fixed non-degenerate simplex of k + 1 points provided d ⩾ k + 1, a result originally due to Bourgain, is also presented. 
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  7. ; ; (, Proceedings of the American Mathematical Society)
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